Live from Las Vegas, it's theCUBE, covering AWS re-invent 2017, presented by AWS, Intel, and our ecosystem of partners. Hey, welcome back everyone here live in Las Vegas, the CUBE's coverage of Amazon re-invent. It's 45,000 people, a lot of action. Again, three days of wall-to-wall coverage. This is day two, trying not to lose my voice. I'm here with Justin Warren, my co-host this week, among the Stu Miniman, Keith Townsend, a variety of other great, great hosts for theCUBE. Doing our, doing our share to get that data to you. Our next guest is Kellyanne Remethan, who's the Vice President of Product Market at Sumo Logic, but also the author with a group of people from Sumo Logic on a great report that they have out called Modern Applications in the Cloud. And he came in, took some time to come from his meetings to come on theCUBE to talk about it, because we've been riffing on what is a modern application, what is a modern cloud. You know that, Justin and I, we were talking about this renaissance in software development. Obviously the cloud wars are happening, the waters being pulled out, that tsunami's coming, it's changing the face of startups, IT, and developers at the heart of the action, a new cultural renaissance. Welcome to theCUBE. Thank you very much. So, little editorializing there, no pining, but we believe that we are seeing a sea change of renaissance in software. Because the things that are now possible, the creativity, the power of developers, the end-to-end visibility into services is just like putting a PowerPoint slide together or Lego blogs, it's just like, it's so easy, not, but I mean, it could be easy, it's easier. Absolutely. So modern applications are top of our minds. So, everyone wants to be modern, they want to be hip, they want to be cool, but there's some serious work getting done right now in the cloud, and there's a shift of greatness coming. What is your report show, because we want to dig into it.  Absolutely. Is Oracle a modern application? Do I buy Watson at IBM? I see that on TV a lot. What is a modern application? Yeah, let me, let me, thank you, John. So let me start with a quick introduction about SumoLogic, so that I can set a context about this modern application report. So, SumoLogic is a cloud-native machine data analytics service, and what we do is to help our customers manage the operations and security of their mission-critical applications, right? The end goal to our customers is that now they can deliver an application with very good security posture and with exceptionally good customer experience. Now, we've been in AWS for about seven years, we have about 1,600 customers under management today. So, what we've been able to do in this modern application report is to fundamentally mine data from our customers in a very anonymous way, and give insights into what typically makes up a modern application in the cloud, right? And when we talk about modern application, I typically see three characteristics to this modern application. First and foremost, many of these applications are indeed architected, or perhaps I should say even re-architected in public cloud environments like AWS, or Azure, or Google Cloud Platform. Secondly, many of these applications are built using DevOps and agile trial practices, so the rate and speed of change in this application is completely off the charts. The third thing that we are starting to see a lot more of is that many of these applications are built using microservices-style technology, so it's very easy to compose these applications. You can put them together very easily, you can make changes to these applications a lot. So, that's our typical definition of a modern application. Yeah, okay. Well, we heard Andy Jassy, I think, one or two days ago was talking about if I started AWS again from scratch, today I would be using serverless. So, I wouldn't be deploying virtual machines, I wouldn't actually be using a lot of the AWS services that we have today. So, what are you seeing in the momentum for how developers are using the different types of stack? So, we're seeing a lot of growth in NoSQL, we're seeing a lot of growth in serverless functions. If I was starting a modern application today, what would my stack look like? Yeah, I mean, that's at the heart of the report that we put together, right? The report actually provides an end-to-end application stack, starting all the way from the infrastructure layer to the applications, and then even perhaps the management and the security technologies that you may need to manage these modern applications well. So, let's start out with the infrastructure layer, right? So, what Sumo Logic has identified, you know, anonymously again, mining our customer data is that, you know, on the infrastructure side, Linux rules as a operating system goes without saying. Linux is the dominant operating system in AWS. And that is to be understood. But here's the other interesting data point, Linux is also getting significant foothold in the Azure world. And that is, you know, not commonplace knowledge today, right? I mean, you would expect that Windows is ruling the Azure world, but we are actually starting to see dramatic year-over-year growth in terms of Linux within the Azure world. Now, let's move up the stack, right? Let's go from the host and the operating system now to the container world. What we are starting to see is dramatic growth in container adoption within AWS. Last year, when we put out the first version of this report, we saw that 18% of our customers are using Docker within AWS. This year, we are seeing that one in four customers are actually using Docker within their environment. NoJS, we saw a new Relic had a report, too. They laid out a little bit different instrumentation of it, they wanted languages. Python with NoJS, certainly NoJS, really awesome for the cloud. And you're seeing that continue to be great. How does that going to fit into Azure, for instance? What are they doing in their clients? So we were talking about Azure, right? So you look at their numbers, right? Azure versus AWS, OS adoption. Okay, Linux is moving up because they made that announcement. But people have been looking at Azure and confused by the Azure stack. It's almost like a black box. Here, Amazon lays it out very cleanly. How has the Azure stack piece impacted? You know, Microsoft, you know, they have historically been a much more of a close ecosystem. But I think in the Azure world, we are definitely starting to see Microsoft open the Kimono in some sense and start to adopt, you know, not just open source technologies, but also technologies that are not very core to the Microsoft stack itself. A lot of our customers who are using us in Azure today are, as I mentioned, they're using Linux in a fairly significant way. We are also starting to see Azure functions being used in a significant way. In terms of the entire application stack, again, Azure has, you know, while they are behind AWS in terms of the number of services, the richness of the services, we are starting to see them catch up in a very significant way. Here's a pointed question for you. It's a tough question. Maybe tough to answer, maybe you know the answer. A lot of people try to fake it until they make it. Yes. And you've heard that term around.  So what do you see as ones that aren't making it in terms of architecture and stacks? Maybe it's legacy trying to bolt on a little bit of a glam front end, JavaScript or node. Where's the failure or having one relational database, maybe Oracle and trying to blend that in? Is there a formula that you see that's not working? You know, I think the act of just putting on a shim around a legacy technology and calling that modern, I think what we are starting to see more and more of that is that, you know, that is, that can take you so far, but only so far, right? The underlying infrastructure technologies of today, especially containers. And you know, you guys heard Andy Jesse talk about Kubernetes today at his keynote.  Brings a little bit of glacier on things, yeah. I mean, you know, can you get away with it for a year or so? Absolutely. But when you're talking about, you know, dealing with extreme scalability, high elasticity, security of the kind that is needed for most enterprises, that's where the legacy technology and just a sprinkling of dust as you described it is going to fall apart. I love the top two of the three top data are no sequel. Interesting, you got MySQL, Redis, Mongo and Postgres SQL, then Cassandra, and then Redshift.  Absolutely. That's surprising. I always love Redis, but that's moving up. That's ahead of Mongo. Yeah, absolutely. I mean, Redis has a huge following. It's a in-memory database, as you know. It also has a lot of shades of no SQL. It's flexible. It's very flexible, absolutely. So, I mean, the interesting data point in the database analysis that we did was that in the cloud world, no SQL and SQL are pretty much head to head, right?  Does it have to be the oracle of the past? Can I re-architect it for something that's more optimized for what I'm trying to do now? And that's where I think no SQL has really caught on. I mean, you know, Justin, we were talking yesterday and Andy's keynote added one-on-one with him a week ago. It's good that some of my content made into his keynote because one of the things that I've been banging on, we talked about yesterday was these modern databases, modern apps could have multiple databases. And you look at Redis, there's different use cases. You know, DynamoDB is slow on look-ups. I might want to have a queue there. I might want to tie it with Redis in a little bit of architectural shape. It's a whole new normal. It's not a rhetoric pony. Yeah, Redis is really popular in the Kubernetes community, I know. So, as we see Kubernetes growing, then I expect that the Redis growth will also follow that. The question is, and he put on his keynote was, the new modern app can have multiple databases. This is going to have a huge impact. How does that impact this report? What are you seeing? Because now it kind of changes the game. It's not one, it's not just, can't just throw MySQL at it or Mongo. It used to be the old days Lampstack. I can say, okay, Mongo is awesome. I'm going to build my app and now I've got to integrate it with another app. Yeah, now absolutely. I mean, you know, we're seeing heterogeneity across the board, right? And that is part of the goal of a report like this too, right? I mean, we put this report out mostly focused on cloud architects, DevOps engineers, SRE engineers who are rethinking what it takes to run an application in the cloud, maybe AWS, Azure, et cetera. And we wanted to provide them a roadmap of what are their peers doing in this world? Well, we really appreciate you, Sumo Logic, doing a report. New Relic has one. We love these kind of reports of them and they're this good. We'd like to talk about them. I know you're being really nice and you don't want to lose customers by pissing off other cloud guys because you're in Switzerland. You play with all of them. But there's really some interesting data here that points to who's leading and who's not. And then the stacks do matter. The developers are influencing IT decisions now. So knowing the stack, knowing your stack, what works for developers, super important. We're going to keep track of it. We'll certainly invite you into our Palo Alto studios to do some check-ins on the report. Maybe do a deeper dive, appreciate it. Yeah. And all I'll say is this report is available on our website. It's, you know, you don't have to register. You get it. Free. They only have it for an email address, which is great. So thanks so much Sumo Logic. Thanks for coming on theCUBE and breaking down the report. More live coverage here from Las Vegas for Amazon re-invent. I'm John Furrier, Justin Warren. We'll be right back with more after this short break.


Tragedy struck in Emo State on Tuesday as yet to be identified gunmen open fire on traditional rulers killing two of them in the process. The traditional rulers were having a stakeholders meeting at the council headquarters at Nenasa in the Injaba local government area of the state when the Hulam struck. The affected monarchs were Eze, Ie, Durubere, Obi-Wan of Okudo and Eze Sampson of Ihebunowere autonomous community. Meanwhile, the Emo State governor, Hupuzodimma, said efforts have been made to fish out those behind the killing of the traditional rulers at Injaba local government headquarters on Tuesday. Well, the situation is very pathetic. The situation is condemnable. This is a new dimension to the banditry in the state where they have to now begin to attack traditional rulers gathered in a hall, a normal meeting where the council chairman presided. All I know is that we will take it very seriously and we must go out to every length to ensure that those behind that crime are brought to hope. We will never allow such a thing to happen again in the state. Hello, hope you enjoyed the news. Please do subscribe to our YouTube channel and don't forget to hit the notification button so you get notified about fresh news updates.


Okay, we're back everyone. This is the wrap-up of day two of exclusive coverage of SplunkConverse.converse2013. This is theCUBE, our flagship program. We go out to the events, instruct the city from the noise. I'm John Furrier with SiliconANG. I'm joining with my co-host Dave Vellante, and Jeff Kelly has been out scouring the landscape today. Guys, we're going to put a bow on this event. What a great event. Coming down to our final segment here. Let's wrap up the show, Dave. I'll start with you. Observations, I mean, we heard a lot of great guests here. Today, a lot of customers. We had a few Splunk folks come in. We had security. We had the senior vice president of business development. Big smile, spring in his step. Business is good. What's your take on the SplunkCon? Well, I just want to say, John, first of all, I feel really privileged to be able to come to events like this, work with you and work with the CUBE team. We've done three events now this year. They're really, they're small, but they stand out for their passionate customers, their innovation, the vision of their leaders. The ServiceNow Knowledge 13 conference, the Tableau Customer Conference. And now the Splunk.conf. Those three events were unique in that, as I say, they were small and intimate, yet at the same time, the customer base is highly passionate. It's a 10x value proposition. It's very exciting. And it's a privilege to be invited to these shows and have the CUBE here and document them. I think my second point here is, it's not uncommon at these types of events that you hear a lot of talk about product because that's what customers are used to. That's what they want. They want innovation around their products. So we heard about Splunk Enterprise, version six, we heard about a new cloud offering and we heard about HUNK. I think version six is no brainer. That adoption is going to skyrocket and that's Splunk's big opportunity. I think cloud and Hadoop are longer-term plays. There's a lot of experimentation going on there, but I think they're both highly strategic for Splunk. As you were saying earlier, John, Splunk is really starting to spread its wings. It's starting to bump into a lot of adjacent markets. It's going to get really interesting here as they expand their footprint. And I think the third thing is I've said that I think coming out of this show, assuming the government starts up again and October doesn't blow up, I think Splunk's going to have a nice halo effect from this conference. I think the biggest thing I've heard from customers at this conference is, wow, there's a lot more things I should be using Splunk for than I'm currently using Splunk for. That means you're going to see, I think a good calendar Q4 for Splunk. You're going to see a big uptick. I think their fiscal year, they're going to do close to $300 million this year, if not break $300 million in revenue. The thing that I'm watching really is the ecosystem and the channel. I think that Splunk's doing a great job there, reaching out to developers. That to me is the big indicator of success. How much more leverage can Splunk get out of its ecosystem and its channel? Can it get that number, which is 45% of the transactions today going through the channel? Can it over time get that number up to 75%? I believe that's where it has to get. You know, Dave, I do have to agree with you, one, the channel, watching that is key. I want to add to your observation, which I agree 100% with, that the thing that stands out for me at this conference in Splunk is they've cleared the runway with the IPO, the growth, they have that under their belt, they're not looking back, and they're growing. So like clearly that's the business side of it. But the things that stands out and makes Splunk a special company is the people and the products. The people are passionate, they use their own product, they are geeks, they're users as well, and the products that they built are solid. But the thing that I think is going to make them such a killer company, in my opinion, is that they've cut their own path. They're doing it their own way. They're not trying to be a BI company, they're not trying to be in a data warehousing. They're taking their own path. And if you look at history, all great companies have a platform. And these guys have so many use cases being generated by their customers, Dave, we've heard that, that people are making up new use cases all the time and they're not making it up. They're actually delivering solutions and it's not even Splunk. So there's a lot of leverage in that platform. I love what you're saying there. That's the definition of a platform. You're right on there. That's the definition of a platform. And you look at what happens to companies like this. Did Splunk execute amazing competitive strategy? If you look back at it, you say, hey, you know that's amazing competitive strategy. You pick a segment in the market, IT log files and sequenced to a broader market position. That's competitive strategy 101, that's how you grow the market. I think they did it by accident. And if you look at great companies, Dave, great companies like Google, accidents like that happen. The being lucky is about being in the right place at the right time. I think Splunk has a Google feel to it. Whether you call it by accident or just good timing and good luck with big data, Splunk is in that position of a platform. They're enabling a lot of different solutions, driving a lot of revenue, a lot of leverage. If they get the channel right, if they get to go to market and the flywheel and the sales side going, it could be nothing but net for these guys. I would agree with you, John. Sometimes you got to create your own luck. So, I mean, you got to give a lot of credit to the team here, as you said. Some really smart, innovative people. They really stuck to the plan the first few years, focusing on their core mission, machine data, log data analytics and monitoring. And now they're really starting to expand, as you said, and becoming a true platform play. We're seeing customers out there talking to one another. I've had several on today who said the best part of the show is going into some of these other customer sessions and just learning from my fellow Splunkers, Splunk users, I should say, about some of the things they're doing and things I haven't even thought of. So, the ability to land and expand, if you will, and apply the platform to any number of areas is certainly so far a winning strategy for Splunk. Again, something similar to what we see happening at Tableau, but as you said, Dave, as they kind of spread their wings, they are going to start bumping into more competitors. Even Tableau, for instance, there's a little overlap there with the types of data visualizations you can create. So, Dave, I want to ask you a question, because I mentioned this in our last segment. Suck an exhaust, a data exhaust from the market, I call that, I don't want to say the bottom of the barrel, but the food chain clearly is up on the high end with the business value that Splunk is clearly executing on. That's the big leagues. How do you look at that? We talked about it in the last segment. What markets are they jumping into? Does this compete with ServiceNow? They're going to get into the IT service management. They're talking operational analytics, is that IT? Clearly, IT is a focus. What's your take on Splunk? Just cut a path through three, four markets, or who do you see them bumping into? Well, I definitely, I see them bumping into VMware. Basically providing what appears to be a better tool for monitoring VMware than VMware has. I definitely see them bumping into the traditional BI space. No question. I see them, even though I think they're partnering, I see them bumping into the visualization space.  And now it's going to be really interesting with Hunk to see the adjacencies in Hadoop, because what we heard from Splunk is what they're doing is not just Hunk for Hadoop, that's where it's starting, but they're really driving it into that big data, what Sean was talking about, that big data ecosystem beyond just Hadoop, laying Hunk on top of Hadoop clusters, but also bringing a federated Splunk, if you will, going where the data is. To me, that's the right model. What's, the other one says, oh, Hadoop and big data. Hadoop's not big data. To me, what Hadoop sort of defines the paradigm of big data because it's all about leaving the data where it is and shipping the function to the data. And that's not a use case that works all the time, but for an increasing number of use cases, it's very effective because there's so much data and you don't want to move it. So that's kind of my take on some of the adjacencies. John, anything you'd add to that? Yeah, well I want to add, but yeah, certainly I'm not trying to add to your commentary because it's awesome, but I want to get Jeff's take on the Hadoop piece because before I add on, because what's interesting about Splunk is the challenge is, do they increase the product feature functionality? We ask the VP of product management this, or do they go in and support multiple data sources like Cassandra, you guys brought that up earlier. Jeff, this is clearly big data. They're trending in the big data space. Our CrowdSpots dashboard showing number four trending item in the big data vertical of close to 690,000 people that we're monitoring on our panel. What's your take of Splunk's impact on big data? The big data goes, I'm talking about Apache Software Foundation. We're talking about generic kind of the Hadoop summit, Hadoop World Crowd. Well, so we've done some research at Wikibon and we've found that the return on investment in big data deployments and specifically around Hadoop is not getting to the level where people expected at this point. People, for every dollar invested, they're only seeing a return of around 55 cents according to our research. One of the reasons for that is that they don't have the tools to either build applications that allow them to extract value from the data that you store in Hadoop or they just don't have the off-the-shelf applications available to them. Splunk has an opportunity to parlay what they've done with log data and apply that to the larger big data ecosystem be it Apache, Hadoop, Cassandra, even Mongo. As Dave said, take a federated approach where you're actually allowing developers to build applications across data sources. If they can nail that, that big data market is begging for an application development platform that makes it easy to do that. If they can apply their Splunk platform to these big data sources, they're going to hit a home run. You know, Dave, add on to your comment about my question around what they're bumping into. I mean, this may be contrarian, certainly it's out of the box, but here's my vision on Splunk. I think Splunk is in a unique point in time right now where they are a different animal than no one's ever seen before. I mean, this is a company that has a lot of trends behind their back that is, we're talking about consumerization of IT. This takes the traditional enterprise focus off the table. If you look at search, for instance, you've got Google pure play consumer search. You've got on the enterprise side, you've seen in Deca and a variety of the handful of companies that got exited. They all kind of found their home and information governance, information management, structured data, legacy data sources, you know, pretty boring standard search, enterprise search. I think the new market is not even about any of those. I think it's more like Google, less like an enterprise search. So I think Splunk could use the search leverage, the fact that they have such a great platform and one of their key values of ingesting data and becoming a de facto standard for application developers. They could literally flip the game upside down and become the standard for what we're now talking about this big data application economy that's never shown up. I mean, Mike Olson two years ago predicted that there'd be a tsunami of big data apps. There aren't. That's a fact. It's just analytics and some, you know, efficient visualization outside of those two. There's no killer app. Splunk could be that platform and then essentially use search as a lost leader to get huge market share. So I think that could be, that's a Google-like revenue outlook if you want to go on the high end scenario. It's a great observation. I mean, I think that we were talking earlier to me when Oracle paid up a couple billion dollars plus for InDecca, it was just sort of a signal that search was going to be embedded fundamentally in every application. We were at Oracle Open World last week. We didn't hear one word about InDecca. Nothing. That filled the product hole. That was just nothing. They're making it, you know, fundamental to the app. And what you just described, the potential of Splunk is to, you know, permeate throughout the entire application ecosystem. I think it's a very powerful analogy. I mean, there would be a fabric of IT, right? So, which is now consumerized, right? So if you look at IT with connected phones, I mean, literally it's only like since 2007 since the iPhone hit the scene. So if you go forward, we're still in like, well, you know, diapers relative to the mobile devices. So if you look at the mobile connected and now sensors, you have a completely different paradigm on how the data architecture is moving. We're seeing that with Flash and converging infrastructure. So I think that, you know, Splunk could roll the dice and throw a Hail Mary on first and goal, right? So here's the thing. So here's the thing, we've been talking about these companies for all week here. Guys like ServiceNow, guys like Tableau, guys like Splunk, certainly Workday and some others that you can put into that category. But these relatively small companies that are public, they're growing at between 50 and 80% a year, some even 100% a year. They've got anywhere from, let's say, four to $16 billion market caps, you know, so they're getting substantial. Can they remain independent? Because I mean, I almost cried when three-par got taken out by HP and saw data domain go down. You saw all these acquisitions going. It would just be so great to see these innovative startups, these disruptors, these irreverent companies stay independent for a decade or two decades. We're waiting to see that. Jeff Kelly, do you think that will emerge in this whole big data marketplace? I think there's the potential for two or three of these players to potentially stay independent for at least longer than maybe we thought. And that's the problem, there's potential for the potential, right? But, well, let's look. So some of the big data players that have not gone public yet are probably going to do so in the next two years. Cloudera, Hortonworks, Datastax, and MongoDB, I think are all going down that path. One or two of them will probably get acquired, maybe even before they go public. Two that go public have a potential.  The other, I'm guessing we'll see an acquisition. Maybe an Intel will make an acquisition. Oracle certainly might make an acquisition in this space. Oracle's strategy around big data is just so backwards right now that they don't know how to handle that. So Dave, go back in time, okay, or at the beginning of the year, stock price on the 52 week low is 26. April is 39 and it's up at an all-time high now, trading at the high end of the range. It's down a little bit today, but in the 60s, 62 up there, it's around that number. And so, you talk about only a market cap of six billion. If they continue to roll out and become a standard with the kind of use cases we're seeing, this thing could easily be a $200 billion company. I mean, we're talking, that's a Google-level run. If they can, on the high end of our scenario, if they did, that's a $200 billion company. Look at Facebook, look at some of these other companies. Look at VMware. I mean, look at the market cap of VMware and look at this company. So, with all that leverage, it begs the question. It begs the question, if the game can be flipped around for app developers, just the little conversation we had about MongoDB this week has been interesting, right? Mongo's in the conversation. Internet of Things is in the conversation. So, they're cutting through multiple trend lines here, so. Well, they have a huge opportunity with the whole industrial internet play. I mean, that's all about connecting machines and making sense of that data. I mean, as you said, Splunk could apply the tech there, platform to any number of use cases and emerging markets. Well, I think, again, Splunk, ServiceNow and Tableau, to me, all have the potential. I think all three will be billion-dollar companies. I think they're on that trajectory unless they screw it up. What are their risks? Internal execution, I think it's the big one, obviously. There's competitive risks, and of course, if somebody takes them out, they won't get there. But I think all three have the potential, which is, well, I hope they don't sell out before they get there. And then, of course, what happens is, at some point, their market cap gets so loud, they do become acquisition-proof. And that's where it gets interesting, right? And it's hard for a company, when they're in that range, kind of NetApp went through this, and they're sort of going through that cycle. Again, they're too big to be bought, right? The value's there. I mean, look at what autonomy was bought for by HP. I mean, look at the number. We don't even go there in terms of the conversation, but you're talking about $11 billion, right? I mean, that was what they paid. Now, I'm not saying that HP should buy these guys, but if you're Microsoft, or you're anyone in the IT business, and you just say, man, offer 10 now and help they take it. You know? But they have to keep funding innovation. They have to expand internationally. Here's the deal. Right now, these companies don't have to be profitable. So they can very effectively compete with the likes of Oracle, and IBM, and HP, and EMC, and the others, because these companies don't have to be profitable. They have to throw off a little bit of cash, but they can lose money, and Wall Street will keep rewarding them for growth. As long as you're on that growth trajectory, you have a unique advantage in the marketplace. It's when this growth slows down that the pressure for profits hits. Now, and Jeff Calubin hammering on this for months now, when these companies go public, that's really when, so I'm not worried. Growth is like a heat shield for these companies. It's when the growth slows down, you know, below 50%, 40%, they start growing at 20% per annum. That's when the pressure for profits really starts getting ratcheted up, and then they got to make tough decisions. Do I invest it in R&D? I got to ratchet that down. Do I, can I expand internationally? Were there's huge opportunities? That's when it gets really interesting and really tough, and that gets to be around when they start getting close to, you know, 600, 700 million toward a billion. So it's going to be really fascinating to watch. Absolutely. Okay, well that's a wrap. Any other comments, guys, you want to share? It's going to have time to wrap this up and get back on the road. I'll be going back to Palo Alto, you guys back to Boston. Thanks to everyone. So, let's see, so we should tee up the fall schedule here. Right, our next big event is going to be the end of October, big data NYC, same week as the Duke World. So we are going to be set up at the Warwick Hotel, 59 second walk, literally, from the Hilton. So we got a big cube set up, two and a half days at the Warwick. We got a full lineup going, great guests. We're going to have a party on Tuesday night. We're very excited about that. Yeah, and we also, that's a really big event. Strada, the Duke World will be out there covering that event as part of our big data NYC. Follow the hashtag, pound big data NYC. We're going to start pumping a lot of content on there. Look out for our crowd chats. I want to thank Splunk executives and all their customers allowing us to be here and the team, Alex, Andrew, Mick, Jeff Frick, Jeff Kelly, guys, thanks a lot. It's been a great, great run here. Two days, second year in a row for Splunk Conference. This is the cube. This is a wrap up live. Wrapping up here at Splunk Conference 2013. See you at the next show.


So, this lecture is on computational heat conduction. So, we started with introduction then moved on to grid generation and then we will start with heat conduction problem. So, pure diffusion problem and I will start with finite volume method for heat conduction problem. So, there I will show you how to obtain linear algebraic equation from control volume using certain approximation. Then I will talk about the two different methodologies solution methodology explicit method and implicit method, thereafter I will discuss implementation details how to convert it into a code. I will be little more detail as far as code development is considered in this topic as compared to the grid generation topic. Finally, I will discuss the solution algorithm and then I will show you some example problems. So, this slide shows that the finite volume method which is being discussed uses an approach which is different from what you see in what you see most of the CFD books. This is what you teach in your undergraduate fluid mechanics for heat transfer, how to obtain governing partial differential equation which you call as the Navistok equation which includes continuity as well as momentum equation. So, from control volume in undergraduate courses typically student learns how to get partial differential equation. Now, when you go for CFD you are interested into algebraic equation. Now, what you see that in most of the CFD books in fact all the CFD books they start from this governing partial differential equation and they show you how to obtain the algebraic equation, but the same set of algebraic equation can be also obtained from control volume. This is what will be shown here specially I had found that for the undergraduate students as we had discussed yesterday that many colleges you say that they have you have CFD course for undergraduate, but the students are not taking it up and one of the major reasons you feel that they feel it is quite mathematical they find it specially they are it is offered as an elective in the last year and the students go for easier option. So, in this we will follow an approach which is not that mathematical although some mathematics will definitely be involved. So, we start with control volume. So, rather than starting. So, the difference is rather than starting from differential equation we start with some picture some control volume and reach to the differential equation. So, this is we discussed in this course. So, this is the plate of length l 1 in the x direction l 2 in the y direction and this is the equispaced vertical lines equispaced or simplest form of the grid generation for heat conduction in plate and this is the centroid of the plate which is the cell center for finite volume method. So, there are 25 yellow circles which are the interior points for the plate. So, let us suppose you are interested you have taken this plate from a furnace at let us say 200 degree centigrade and it is subjected to certain thermal boundary condition. So, let us suppose left wall is subjected to 100, bottom wall is to 200, right wall to 300 and top wall to 400 degree centigrade or there is a boundary condition. So, you want to determine the temperature distribution. If you are doing an unsteady simulation you can create even a movie of the heat transfer. This is a typical computational stencil which is involved in the electric equation. This is the boundary control volume, border control volume this I had discussed in my previous lecture an interior control volume. In the last lecture we had shown you how to obtain the x and y coordinates of the vertices of the control volume. Once you know that you can calculate certain geometrical parameters which will be coming in finite volume method. What are those geometrical parameters? Width of the control volume in the x direction in the y direction the phase center. We have four phases earlier I was saying left phase, right phase, bottom phase, top phase. In CFD we call them as west phase, east phase, north phase and south phase. Then you have certain neighbors. So, a small letter this small w represents phase center capital W represents west neighboring cell center. This is south cell center, east cell center and north cell center. Other than the width of the control volume you also need the distance of a cell center from its neighbor which is used in calculating the temperature gradient at the phase center. So, once you know the coordinate of the vertices from the grid generation you can obtain the coordinates of the cell center. Then you can obtain the width of the control volume the distance between the cell center and its neighbors. Width of the control volume you can calculate through this expression surface area you can calculate through this expression volume you can calculate this expression. These are two-dimensional control volume. So, this geometrical parameters are later on I will show you that they will come as a coefficient in the algebraic equation. In grid generation after we obtain the coordinates of the vertices we obtain this parameter because this parameter will come into the algebraic equation as coefficient other than the thermo physical property. So, in my first lecture I showed you how from a control volume how to obtain differential equation. Now, in this second lecture what we will do is that we will not start from differential equation. We start from the same control volume and learn how to obtain an algebraic equation. What is the law of conservation of energy? Rate of change of internal energy or enthalpy of solid inside the control volume is equals to heat gained by conduction which is total heat inflow minus outflow plus heat gained by volumetric heat generation. So, total heat gained is equal to rate of change of internal energy. So, we start with certain words now we have to convert this words into algebraic equation earlier we had converted into differential equation. Now, let us suppose take this room and if you want to represent the rate of change of internal energy of the fluid inside this room. Rate of change of internal energy of the fluid inside this room let us suppose temperature inside this room is varying with respect to time. So, if you take one point temperature is varying with respect to time. How do you represent rate of change of internal energy? How do you represent internal energy? Mass into specific heat into temperature this is internal energy. If you want rate of change time rate of change and you do the temporal derivative. So, del by del t. So, rate of change of internal energy is equals to del by del t of rho into volume this is mass specific heat and temperature. If the fluid is incompressible density will not vary with respect to time specific heat does not vary with respect to time. If you take a fixed volume this will let me put it like this strictly speaking this can be expressed like this rho C p volume integral of del capital T by del small t. Do you agree with this? This rate of change of internal energy rather than writing like this I can write it as a volume integral. Because this rate of change of temperature varies from point to point in a volume is correct. In this room you have infinite number of points and at each point this term is varying. So, you can write it as a volume integral. So, in this you have to use mathematics to calculate this term. What is the variation of temperature gradient in space in a volume? Let us say in this room you have you put some temperature measuring instruments and let us suppose wherever you are sitting just at that location measure the temperature with respect to time. So, consider each one of you as a control volume. So, it will vary from point to point, but if I say that out of let us say 50 people I want to take only one value which value I should take who is sitting where in this room that corner that corner of front centroid. Anybody anyone would like to say with a different answer to this? Corner anybody would like to prefer or front or back or centroid is good enough. So, who is sitting at centroid? The cameraman is sitting at no. Why centroid? Let me ask you that question that approximation will be good that will depend on the size of the room or not. It would be good approximation on large size room or small size room that is the mathematics which is involved. If you understand that this understanding is very much similar to I will give you an example. Let us suppose you see a curve when I said volume the variation is with respect to volume, but for simplicity I am just showing you temperature or some function is a function of x. Let us suppose this function is varying in a very non-linear fashion. This centroid which you are saying is basically a linear approximation what you are using assuming is in this room in this volume the variation is linear in all the direction x, y, z direction. So, the idea which we are using is very simple. Instead of that volume if you take certain distance element in this region what is although let us suppose this function is varying from here to here, but if I want to represent by one point value what is that best one point value? Suppose this is x 1 this is x 2 I want one value in between x 1 to x 2. So, which location temperature you would like to prefer? At the middle. So, this middle or that centroid which you said is the same idea mathematically. So, you can if you can understand this curve. So, here what is varying is temperature gradient in a volume here this is a just a function. In CFD note that we use some approximation, but that approximation is good if your size of the control volume approaches 0 it is very small. That is why you want to have large number of grid points. You want to have very small volumes because smaller is the volume better is the approximation. And this idea is very much similar to what you study in your schools that a function may be very non-linear, but if you take very small part of it its variation is almost linear. This is the level of mathematics which will be used in the approximation. So, the first level of approximation is the average value of this temperature gradient in a volume is equal to the value at the centroid. So, the first level of approximation is in a volume I showed you earlier I had shown you here. In a volume the change of this what is this term rate of change of temperature in this volume. So, we need to do volume averaging of the rate of change of velocity in case of, but here it will be only temperature. Volume averaging of for the rate of change of temperature in a control volume as a value at the centroid. This is what we discussed just now. This is what is order of this approximation. This is mathematically it is called as second order approximation. Now there is a second level of approximation. The first level of approximation is volume averaging of rate of change of temperature. The second level of approximation is how I can obtain this del capital T by del small t in algebraic form. If you know finite difference method and time is much in the forward direction. Always whenever you solve a unsteady problem you have an initial condition. From initial condition so typically let us suppose you want to create a movie of flow or heat transfer always you have a situation you know the initial picture from initial condition and boundary condition. From initial condition you obtain the picture for let us say if your time resolution is 1 second using the picture of 0 second you obtain the picture for 1 second. Using the picture of 1 second when I say picture it is not only pictorial information which is used in the codes which is the fluid dynamic information like velocity distribution, pressure distribution. So, time always marches in the forward direction. So, here one first order approximation is that we do forward differencing in time. This is derivative with respect to time we use superscript for as running indices as i, j are running indices for x and y direction n is the running indices in the time direction. So, we do forward differencing and represent this temperature gradient as T at 10 plus 1 minus T at 10 divided by delta t at the centroid. So, this centroid representation first we this is the first level approximation volume averaging in the second level we do first order forward differencing. These are the two approximations which are used to represent the unsteady term as this. Any question on this? Mathematically how it can be said that the first level of approximation is the second order approximation. Later on when I will be discussing the advection schemes there I will show you mathematically that it is second order accurate. When I will be discussing the central difference scheme because this is like a central difference scheme where you are basically type doing some type of averaging. There mathematically I will show what we will do is that we will take a quadratic curve and then show that it is a second order accurate. Any other question? So, this is the you have a question finite volume method discretization of one term which term is this unsteady term. Right now I am showing it for rate of change of internal energy, but we will use the same thing for rate of change of x momentum rate of change of y momentum. Same approximations are used there also. Now let us go to the diffusion term. What is diffusion in conduction? Conduction heat transfer. So, what you do in heat transfer course you have q x, q x plus delta x, q y, q y plus delta y. But here now when I am doing when I am in CFD I will not write this as q x or q x plus delta x because I want to write this q on this surface as one point value. What is the best point? Earlier we talked about volume, now it is surface area. Answer remains and is there answer different or same. If I earlier my question was that I want to represent in a volume some function. You said that the best point is centroid. Here again in CFD as CFD we use a discrete method. So, we want to represent the variation as a one point value. What is the best point? Centroid of the surface area which is shown here. This small e is the centroid of the phase, east phase. So, the approximation which we are using is surface averaging of heat flux at the control volume phases. How do we represent in general the rate of heat transfer? Let us suppose perpendicular to this wall the length is unity. So, earlier I had shown you this is volume integral. Here it is actually surface integral, but in the z direction the length is unity. So, that is why I am because this q is varying with respect to y in general. As in earlier case your temperature gradient was varying in volume point to point. So, here point to point this heat flux is varying is the function of y and in the z direction length is unity. So, total rate of heat transfer can be written as integral of q d y where what will be the limit of this sorry from this y y s e to y n e. This can be expressed as average value multiplied by delta y and what is this average value we are taking centroid value. Similar thing we do at other phase centers. So, this is expressed as q n where any centroid of the north phase, east is centroid of the east phase and so on. This derivation is analogous to del by del x of q x plus del by del y of q y. Do you agree with this? When you teach conduction you also start with this q x, q x plus delta x, q y, q y plus delta y. You do a balance. How do you write this q? You write as q x into delta y. This is q x plus delta x into delta y and when you do the balance you write del by del x divided by volume anyway del by del x of q x plus del by del y of q y negative of that. That was differential form of the diffusion term and this is algebraic form. There is no differential term here. What is this term? This is q e into delta y. Here we are doing a balance where is in minus out. So, it is q w into delta y plus q s into delta y minus of q n into delta x minus of q e into delta y. So, this is an algebraic equation. It is not a differential equation. This completes the first level of derivation, first step of derivation analogous to del by del x of q x plus del by del y of q y. What is the second level of derivation in undergraduate courses of it transfer? How to obtain del square t by del x square plus del square t by del y square from del by del x of q x plus del by del y of q y. So, you use in the second step basically you substitute Fourier law of it conduction into that first derivative and then that first derivative gets converted into second derivative. Here the second level of approximation is we will do the same thing. Here also we will use a Fourier law of it conduction, but the difference is Fourier law of it conduction is in a differential term. We have to express this in algebraic term. This is the second level of approximation. So, the second level of approximation is discrete representation of Fourier law of it conduction. Let us suppose this is q e. This q e is actually in which direction x direction normal direction. So, it will involve d t by d x. So, to obtain d t by d x what you do? You draw a horizontal line. If you draw a horizontal line what you are finding? That horizontal line is intersecting this point and this point. So, your face center is lying it in between two yellow circle and you have to calculate gradient in that direction only. So, this becomes d t by d x equals to t capital E minus t small p divided by this delta s e is a distance between this two yellow circle. By finite difference method which is this what is this expression? You want to calculate gradient at a point using one point behind one point ahead. This is called as what central difference is. What is the order of accuracy? Second order Taylor series expansion I had shown in the previous slide. So, this is a second order finite difference discretization. Actually, when you want to calculate gradient here you do the same thing at all the phases. So, here if you want to calculate you take temperature here minus temperature here divided by the distance between the two points. Similarly, here but this type of variation basically what you are assuming is that between two yellow circle the variation is linear. That is why you are using this expression. So, but you are not making sure that there is a continuity between the linear relation. So, that is why it is called as piecewise linear approximation. If you follow Patankar books he uses this approximation because there is we are assuming linear variation between two yellow circle. But we are not sure that the linear variation between this two yellow circle and the next two yellow circle the slope is same. That is why we say that the variation is piecewise linear. There is not continuity in the linear slope of the variation. There is a discontinuity. So, this is the piecewise linear second order approximation. So, we have two levels of approximation. By using first level of approximation we get equation similar to del by del x of q x plus del by del y of q y which I shown in the previous slide which is this equation. What is the approximation we do surface averaging of the heat fluxes. And this is the second level of approximation where which is a discrete representation of normal gradient of temperature at the phase center. Note that this is a discrete representation of normal gradient of temperature. Then what you do in heat transfer you substitute this Fourier law of heat conduction into del by del x of q x plus del by del y of q y. We will do the same thing here. We will substitute this into this expression. Once you substitute you get this equation. What are the different terms? This is the rate of change of internal energy. What is this n plus 1 is the new time level. This is the old time level. And what is this term? This is the rate of this is total heat gained by conduction. And what is this term? This had not used any approximation. This is volumetric. It is per unit volume.  Now, there are two types of method one which is called as an explicit and second is an implicit method which basically depends upon whether you are calculating this total heat gained by conduction using the temperature of the previous time level or the new time level. I will give you an example. Let us suppose you took a plate from a furnace at 250 degree centigrade. Let us say you have subjected that plate to a boundary condition. Let us say left wall 100, bottom wall 200, right wall 300, top wall 400 degree centigrade. So, you know the initial temperature distribution. So, you know the initial picture of let us say if you want to create a movie of temperature variation. Now, when you use this temperature in information, initial and boundary condition information, there are two approaches. One if let us suppose in this case I use a temperature of the previous time level. So, in this how many unknowns I have? So, all the temperature values which have superscript n I know from the previous time level. When I am just starting I know from initial condition. So, then in this how many unknowns are there? 1 sorry which is this one. Let us suppose in a problem there at 25 yellow circle you will get 25 equations, but in each equation there will be only one unknown. This is easier to solve because each equation can be solved independently. This is explicit method. So, I am writing separately this is the unknown which you want to do and these are the neighbors. I will show later on an animation stencil. So, you get here the equation is simple, but there is a price which you have to pay for. I will discuss that little later. There is a second method where this total heat gained by conduction is calculated using temperature of the same time level. Now, the problem here is let us suppose if you have 25 points you have 25 equation, but in each equation there will be not more than how many unknowns? How many neighbor comes into the expression? 4 neighbor and the center point and if all the neighbors are yellow circle and the center point is also a yellow circle. Then you will have maximum number of unknowns which is 5 unknowns, but if some neighbor is blue circle it is a boundary point and that point let us suppose it is a boundary condition then there will be less number of unknowns. So, in an implicit method in a two dimensional problem you get set of equations which are coupled. You cannot solve each equation independently. So, this has to be solved in CFD one way of mathematically one way of solving is that you take the inverse of the coefficient matrix multiplied by the constant vector, but we do not follow that method is called as direct method of solving matrices. Here what we follow is that we solve it iteratively. So, we start with the initial guess of the temperature at new time level of the neighbors and then keep iterating till it converges. For each time level there is a loop for when you do an unsteady simulation there is one loop for time that will anyway be there, but in an explicit method you get let us say 25 equation in each equation there is only one unknown. So, you can solve each equation independently, but in an implicit method at each time step you have to solve set of algebraic equation iteratively. So, there is an inner loop involved when you use an explicit method there is a topic called as stability analysis. If you look into book of JD Anderson he has shown the stability analysis using von Neumann stability criteria this what is mean by stability? Stability means that when you are solving for let us say steady state problem the numbers what do you expect in the real world situation the temperature should the difference of the temperature between two consecutive time step should die down if the temperature should reach to steady state, but computationally if your time step is not small enough depending upon grid size and thermo physical property. So, in an explicit method you need a certain you cannot have time step greater than sorry greater than certain value.  So, the difference of the temperature between two consecutive time step approaches towards infinity. So, your numerics is not behaving what it should behave physically. So, from stability criteria one expression is derived alpha delta t 1 by delta x square plus 1 by delta y square should be less than half. So, this delta what is alpha k by rho c p this delta t now becomes function of thermo physical property and delta x and delta y. So, there is a time constraint you cannot use a time you have to use a time less than a particular value there is a limit which you can use like if you want let us suppose in a real world situation you took that plate from furnace and it reached to steady state in let us say 1 hour. If you are using an implicit method you can take a time step of 1 minute and you can do 60 time marching and reach to the steady state, but let us suppose you are using an explicit method and it demands that you have time step less than equal to 1 second and if you use 1 second as the time step you have to do 3600 times of time margin. In implicit method there is no such time constraint whether you are able to understand and appreciate. So, let us suppose you have a plate which reaches to steady state in 1 hour and if the for the same plate you are doing a simulation in an implicit method you can use a large time step, but it is not that you can use 1 hour directly as time step and then from 0 initial condition 1 time I think you should reach to the steady state. You cannot use a very large time step in implicit method, but you can use a reasonably large time step may be 1 minute or 5 minutes, but in an explicit method demands that let us suppose if delta t should be less than 1 second then you have to ensure that it is less than 1 second. But the problem is although let us say explicit method takes 3600 time marching whereas let us suppose implicit take 60 time marching, but for time marching which takes more computational time implicit because explicit you get 25 equation in each equation there is only 1 unknown you can solve it straight forward, but in implicit you have 25 equation with each equation not more than 5 and 1. You have to solve it iteratively per iteration time computational time which is required for implicit method for time step computational time required with implicit method is more. So, let us suppose per time step explicit method takes 1 second and implicit method takes 1 minute then what will happen there will be a break even both will take same computational time. So, it is difficult to say which one is better, but I will discuss the advantages and disadvantages. I will just like to show you some animation of the how the numbers evolve in an explicit method. This is a type of instantial in an explicit method. So, to calculate the temperature at new time level this is function of 5 different values of the previous time step. So, if this point is p then the same point at previous time level and the neighbors. So, let us suppose this is a plate which you have taken from furnace all the yellow circles are at 250 degree centigrade. This blue circles are at 100, this bottom blue circles are at 200, this is at 300, this is at 400. So, this is the initial temperature distribution which you know. Now, the way we have done finite volume discretization that is suppose there is no volumetric heat generation. So, this value in explicit method we get an expression like this where there is only one unknown. For the new time level there is only one point which is coming in this tensile and this is function of the same point it is not south east western 5 point values of the previous time step used to calculate the temperature of the new time level. This you do for, but in this case as I said if there are boundary values also which are used just see that. So, this equation is used how many times? There are 9 yellow circles it is used 9 times, but what will happen only the neighbor should change. So, in programming you can do it very easily how you do? Using loop. So, you vary i from let us say 2 to 5 j from 2 to 5 2 comma 2 it will solve here 2 comma 3 it will go here. So, this animation which has shown this is for 2 comma 2 2 comma 3 and so on. So, this way I am showing you that this set of algebraic equation in a loop how it evolves with respect to time 5 values are picked up from previous time level and the new time level value is obtained. This happened behind your computer screen after this what happens? So, let us suppose from 0 second you have obtained the temperature distribution for 1 second.  So, you have pictures for 0 second 1 second 2 second 3 second till 3600 second. Then what you can do? You can club all this picture in a sequence and create a movie. This I showed for heat transfer the same thing happens for fluid flow also. In an implicit method what happens? You have a stencil like this what you are finding here is that from the previous time level only 1 value is coming that is the same point value. And in this the stencil is such that there are 2 bonded there you can see that in this stencil 2 blue circles are coming this is 100 sorry. Yeah boundary condition does not changes with respect to time. So, this blue point values will not change with respect to time. So, as I said that this boundary condition is such that this left wall is at 100 and this is at 200. So, 2 values are known from out of this 5 values. So, there are 3 unknowns here 3 yellow circles. If you go to the next point 4 yellow circle 4 unknowns 3 yellow circle 3 unknowns. So, you get self-algebraic equations you have not more than this here you have 5 unknowns. So, you get some equations where are there are 3 unknowns 4 unknowns. Basically the corner yellow circles have 3 unknowns central yellow circle has 5 unknown corner yellow circle will have sorry this yellow circle has 4 unknowns this is a corner 1 it has 3 unknowns. So, you get here set of a yellow equation where there are in this point you have maximum unknown 5 unknown where all neighbors are yellow circle. So, this has to be solved iteratively. So, other than the time marching there is a second loop to solve the set of a yellow equation. Any question into this? Is it occur only in the explicit method? Yeah. So, the question is the stability occurs only in the explicit method the answer is yes and first clarify more I think you need more understanding into what stability is what happens is that there are certain truncation error which occur whenever you solve in computer there is certain precision with which you solve. So, if those truncation error grow with respect to time then your numbers approaches towards infinity. So, with respect to time how this numbers grow if you follow a book on stability analysis you get all these details. So, from there this type of criteria are obtained this type of stability criteria you can mathematically it has been done for pure diffusion equation pure advection equation. But when you go to Ney-Stokes equation it is a combined convection diffusion equation with a source term. So, for that there is no stability criteria. So, when we use the Ney-Stokes equation we do not have any stability criteria for explicit method in Ney-Stokes equation. But what we do is that we take the stability criteria from pure convection pure advection pure diffusion and we use that as a guideline at least we make sure that. So, this is a necessary condition but it is not sufficient for Ney-Stokes equation. Yeah, I will just add to that for your information. There is a very good discussion based on sort of physical arguments in Patankar's book if you want to get some sort of an idea of why a numerical scheme should behave whether it is stable or unstable. It is a very nice discussion and purely based on physical arguments and it is worthwhile reading that it is I think in the chapter number 3 and 4 initial when he talks about heat conduction itself. What Professor Sharma is mentioning is actually what we what is called as a mathematical exercise called the von Neumann stability analysis as he mentioned. Is this a false diffusion? No, no, it is just the maintaining of the positivity of coefficients. Okay, okay, correct. It is a very nicely written set of paragraphs and I think that should help you a little Yeah, in fact I am planning to discuss that when I teach advection the coefficients become peccalite number relationship there is there in the advection maybe I will it is good that you pointed out I will emphasize that. So, let us go to the advantages and disadvantage of the two approaches. The explicit method is relatively easy to set up and program and that is what we are giving you because we want to initially give you programs which are easier to understand. So, the codes which will be there in tomorrow's lap session or conduction are based on explicit method. The implicit method advantage is that it takes lesser step to reach when you want to do as I said if you want to do calculation for 1 hour you can take lesser number of time step you can take let us say 1 minute then you need only 60 time step. The disadvantage of this explicit method is that it may take it is not always necessary that it may result in long computational time make calculations over a given interval of time. So, let us suppose if you want to do steady state computation of 1 hour then if your time step restriction is 1 second then it may take more time, but it is not always true. For a time step calculation computation time is more in case of implicit method as I discussed earlier and for transient problem if you are solving steady state problem probably it makes much sense to use an implicit method, but if you are solving a transient problem where you want to capture true transient in fluid mechanics or heat transfer there are 2 class of problems. First class of problems which reaches to a steady state situation and there are second class of problem which reaches to maybe let us say a periodic flow like if you talk of flow across a circular cylinder there is one vortex shedding phenomena if you have heard of. So, what happens the flow does not never reaches to a steady state, but it reaches to a periodic state. So, with respect to time the vortices break away from the rear side of the cylinder alternatively from the top and bottom. So, for inherently transient problems if you want to capture the transients accurately it is very important that you should take then the time step play important role and then perhaps explicit method not always is more beneficial. And second thing is that nowadays we talk of parallel computing. So, when you go to develop parallel algorithms it is easier to do in explicit app using an explicit app. Now, let us go to the implementation details. So, we have discussed the theory now how to develop code. Now, to develop code I will show give you some figures pictures to give you an idea how to develop code in easier way this is the way the code has been developed which is given to you. This is the simplest form of the grid generation equispaced horizontal and vertical lines. What I do here for to make you explain this in a easier way is that let us say this is the grid point of temperature. Where do we have heat fluxes at the faces? Where do we have heat fluxes in the x direction? Which faces? Vertical faces. This is the boundary points for the temperature. These are the running indices in the x and y direction. So, I am defining green square here represent heat flux in the x direction. Red inverted triangle represent heat flux in the y direction.  A face is common to two control volume, but we want to represent this heat fluxes only by one indices. So, we need to follow up convention. So, we say that now positive faces in a control volume what are positive faces? East and north are positive faces. So, there are you can what I am trying to emphasize here is that we have three variables here temperature q x q y. Now, I will store this in a matrix form. When I store in matrix form there I need a running indices to tag a particular value of the any of this variable. You can have three different running indices one for temperature one for q x one for q y, but that is not good way of programming. Good way of programming is that I use only one running indices for one of the variable and I follow a convention. So, the convention which I am following here is the any green square I have to see that it what is the running indices of the control volume in which it is in the east face. So, the running indices of this green square corresponds to the running indices of this in running indices is j comma i. Similarly, why the running indices of this is corresponds to j this is the convention I am following. If I ask you what is the running indices of the green square which is here this will be at the east face center of yellow circle which is here what is the what is the running indices of that yellow circle here i minus 1 comma j. So, the green square which is sitting here will have q x j comma i minus 1 what will be the if there is a red inverted triangle here also this will be at the north face of j minus 1. So, in a cell there will be two green square on the positive face it will have the same running indices on the negative face here it will be i minus 1 and here it will be j minus 1. So, these are the green squares which are coming now let me ask you if I talk of the points which are inside the yellow circles which are inside the plate how many are they 5 in the x direction 5 in the y direction or these are the green squares how many are they in the x direction in the y direction. Here at this basically green square they are vertical face center right now we are having 5 control volumes in the x direction 5 control volumes in the y direction. So, we have 25 control volume in this 25 control volume what I have shown as green square are the number of vertical face centers how many are they how many in the x direction 6 in the x direction you have to calculate heat flux at the boundary also note that because when you apply the law of conservation of energy you will need this heat flux here. So, how many green squares are there in the x direction 6 how many in the y direction 5 ok just note this because these are some of the numbers which we will be using it in the pseudo code in the next slide. How many red inverted triangles are there in the x direction 5 and how many in the y direction 6. So, there is a interchange green square is 6 in x direction 5 in y direction red inverted triangle is 5 in the x direction 6 in the y direction. How many total circles are there if you take the boundary points also 7 by 7 these are the 5 yellow circles which are seeing and one is at the left boundary one is at the right boundary where you apply the boundary condition. So, including boundary there are 7 by 7 yellow circles and the green squares are 6 in the x direction 5 in the y direction ok. Now, let me ask you a question that when I was showing the discretization I did the discretization first for analogous to del y del x of q x and del y del x of q y. So, I said that in the coding also for you to explain this in a easier way what I the code which I will show and what has been given to you first we calculate heat fluxes. So, to calculate heat fluxes I have to scroll through all this green square. Now, to scroll through green squares I should know what is the running indices what is the running indices of you can know the running indices of any if I want to know the running indices of this green square I need to know the running indices of which yellow circle this yellow circle. What is the running indices of this yellow circle this is 1 this is 2 this is 3 this is j is equals to 3 and i is equals to 1 2 3 4. So, the q x here is i is equals to 4 j is equals to 3 q y here is same i is equals to 4 j is equals to 3 and here it will be i minus 1 here it will be j minus 1 and so on. Now, when I want to scroll through all this green squares this is my first point this corresponds to which control volume this is at the boundary. The way we are applying boundary condition the volume of the boundary control volume is 0 you can assume that this point is centroid of a volume which is having a 0 volume is this ok. The way we are applying the boundary condition we have this is a 0 control volume that is why the centroid of that control volume in the phase center is coinciding this is only possible if the volume of that control volume is 0. So, it is there is only one point there is no if the volume is 0 there will be no east point west point there will be only one point and the running in this is for this point will be i is equals to 1 j is equals to 1 what will be for this it will corresponds to this is i is equals to 2 j is equals to 1 ok. So, i is varying from 1 2 3 4 5 and 6 what is your i max i max here is 7 let me show you ok the way I am showing i max is this is my i is equals to 1 this is my i is equals to 2 3 4 5 6 and 7. So, my running in this is for temperature let me show you for temperature i is equals to 1 and i is equals to 7 is boundary j is equals to 1 and j is equals to 7 is boundary interior points are 2 to 6 in both the direction when I want to calculate q x it is varying from 1 to 6 this is the i for this will be i for this i for this is 6. So, it will vary from i is equals to 1 to 6 or i is equals to 1 to i max minus 1 and in the y direction it will vary from j for this will be equal to 2 2 3 4 5 6. So, in the i direction it varies from 1 to i max minus 1 and in the j direction it varies from 2 to j max minus 1 ok and i max j max are 7. So, it becomes 1 to 6 and 2 to 5 and if you go to red inverted triangle they are 5 in the x direction 6 in the y direction. So, here it varies from 2 to i max minus 1 and 1 to j max minus 1 if you understand this clearly through this picture you can develop a code. So, this is the pseudo code to calculate heat flux in at the x direction i max is 7. So, it is from 1 to 6 j max is also 7 this is 2 to 5. So, this way you scroll through all the green squares this is a to calculate the distance between two cell center what is this x l x l is the coordinate of the cell center. So, this is the distance between the cell center this is the previous time level temperature between the two neighbors this is at the east phase center ok. I will show in the earlier slide this q x how you can calculate temperature of i plus i is in this direction do not get confused. So, this will be p at i plus 1 minus p at i and how you will calculate q i j is in vertical direction note that temperature at j plus 1 minus temperature of j. You will not only use temperature, but in the denominator you will need to have the coordinates of the cell center. This will be x cell center and this will be y cell center. So, if you do use that you can calculate this is the heat flux in the x direction this is resistance between the cell center in the x direction. And this is note that here it is j is varying from 1 to 6 and i is varying from 2 to 5. So, this way we calculate the q x and q i on all green circle and red inverted triangles respectively. So, this completes the you know first aid of differential equation is del vadal x of q x and del vadal y of q y. In algebraic what is the discrete representation summation on west and south phases q into surface area minus summation of heat fluxes into surface area on the north and the east phases. This is the code of that. So, with this you have calculated the heat fluxes. What do you do in sorry this is basically the discrete representation of Fourier law of heat conduction. Once you know this what you do you do a balance. So, for a control volume if you want to do a balance I had told you that on the west and south phases negative phases heat is going in and in the positive phases it is coming out. So, what will be expression for balance q x here it will be i minus 1. This will be q y j minus 1 you add this 2 because here it is coming in you want to get gain of the heat transfer and this 2 you subtract multiplying by surface area. This is what is done here for the x direction surface area is delta y for the y direction surface area is delta. So, this is just the balance and also note that what is the loop here. This you are where you are calculating the balance at yellow circles. This loop is corresponds to green squares. This loop corresponds to red inverted triangle and this corresponds to yellow circle. So, note the loops which you are using. So, you calculate the appropriate variables at appropriate locations. So, you balance it once you have balance it got the total heat gain by conduction. Then you multiply by delta t rho c p v. This is the expression which you have got from the explicit method. Any question into this? In the program you will see let us say in psi lab language which is basically a c type of language. Same loop will be there. So, whatever is shown here you will can correlate directly in the code go back and see once we give the code as well as the slides.


Right, so what are my favourite products of the new releases of 2021? Well, I'm going to put together a what's in the bag and no expense spared. This is what I'd put together right now. So I'm going to start things off with wedges. We'll start off down that lower end of the bag. And for me, the two, the Mizuno ES21 wedges are unreal. Like I said, they're expensive, but don't forget no expense spared. But they do offer a great deal in terms of their quality. They're superb. And the things I like about them are, hey, I love this wide sole. I'm a big fan of that for average golfers. I think I've mentioned that on numerous occasions now. They're like the Cleveland CBX wedges.  They're not quite that, but they help us massively in terms of not thinning and chunking wedge shots. So that's got to be a bonus for us average golfers. But what I like, I like aesthetics on these, but they've got a massive sort of bulbous back end. They'd very much be classed as a game improvement site wedge. But what they've done very cleverly at Mizuno is they've hidden all of that. They've hidden that bulk and mass that from the top line, there's a huge drop off in the way it's chamfered off. So therefore, when you sit at the top behind the ball, you see that top line, you're not put off as you normally might be from that big game improvement style looks. I love the black finish, but I also love the contrast that they've done with the silver finish in the way it frames the ball. Again, if you want more details on this, have a look at the full review because they've also changed that CG point. There's a bit of tech spec in these, which I actually think is kind of ringing true in the practice that I've had with them. So for me, expensive, yes, but real top quality start to the bag. And they're the two wedges, 54 and 58 is what I put in my current bag. Right, next up, I'm going to have a look at the irons and a slightly odd one in the sense that I've got three different types of irons from one range all in the bag. And I've never done that before. So it's obviously a blended set and it would be from the Callaway Apex range, which I think they've done an amazing job this year, Callaway with this Apex range. I think it's just always admired these irons. But this year it's more interesting the fact they've introduced this DCB range. What's worth pointing out, I did a video early on in January, I highlighted these irons as possibly the best club I've tested in 21. And a few people commented, how can you decide this so early? It was because we tested all clubs by then and I still stick by it. These irons are phenomenal. I would start down the lower end of the bag and pitch and wedge through to eight iron. I'd be comfortable enough to put the Apex Pro in the bag. I think this iron looks superb. Out of the three different styles that are within the range, if I could play these right throughout the bag, this is what I'd go for. But we're going to mix it up a little based on recognising your own ability. But from pitching wedge through to eight iron, where you're looking for a little bit of finesse, you're looking for perhaps that smaller head profile, forged iron, tungsten weighting, still got help in there and more than comfortable with playing those irons. And like I said visually, I think they look amazing. But then I'd stop at the eight iron and I'd switch into what would be the standard product and I'd put a seven and a six iron in the bag of the Apex standard. Now again, they go a little bit more bulkier, which we'd expect. The top line becomes wider, the sole becomes wider, but not to a degree that would put you off in any way and perhaps just inspire a little bit of confidence. But again, the idea to blend the sets would end up with being only a seven and a six iron in the standard. And I would have no problem then in going into this DCB product. This was the new range. It was almost like a game improvement style forged iron from Callaway. And it is a little bit more bulkier mass, but it's at an end of the bag where I want that bulkier mass and I want confidence. So when I put this five iron down, I'm not looking for finesse necessarily. I'm looking for help and assistance, longer shaft, less loft. All becomes a little bit more difficult. On the testing, I was hitting the DCB five iron around 190 carry. Phenomenal ball flight, easy to launch. And it's the perfect end to the bag. So I go pitching wedge through to five iron and that's where the irons would stop for me and that's me done. But that whole range, I think what they've done, the ability to blend those three sets is a real winner, I think, this year from Callaway. I've never put together a set of clubs where my longest iron in the bag is a five. So this is all new for me.  But I think that what I've learned over the past few months in terms of this testing is that maybe there is a more favourable bag for the average golfer to put together. So I would go then into a hybrid. And the hybrid would be, and you've already seen the bag several times on the floor. So you know where these are coming from. They're from Ping. It's the G425 series. And again, no secret. I go into fairway woods and that comes from them as well. I think just the overall message throughout my videos is that their star of the show in terms of their range this year has been the hybrids and fairways. Most drivers, I think we've sort of got very much to the limits. Irons have improved, but hybrids and fairways to me are where I've seen marked improvements. And these are phenomenal. I mean, these literally took them out on several occasions on course. We've tested here at Fourgolf. They just do things very, very well. Launch the ball as you'd want it to. There's a adjustability in each and every one of them. So again, masses of options for gapping your bag correctly. So I would go from a five iron into a four hybrid that is currently set at 22 degrees. And I might just strengthen that just a little to get that gap between my five and what would be this four hybrid. Make sure that sits in nice. But like I said, as I've said with the apex as well, stunning to look at. I love the matte black face. I love the fact that we've lost turbulence from the crown. And you just see that matte finish. The three dots frame the ball incredibly well. As does the white faces around the lines around the edge of the ball. They just do everything so well. And again, I suppose on a personal note, I love the Ulta CB shaft as well. So well, as you can see, very positive about the 425 range. And I'll quickly tell you that I would then go to a seven wood. Yeah, I've harped on about these. Well, best part of a year. We had a look at one of these not so long ago. And this one, again, is an absolute weapon. It's just, I can't believe, to be honest with you, how well this thing performed out on the course. It's a seven wood. It's 20.5 degrees in terms of its loft as standard. Again, has that flexibility and been able to adjust loft. So again, fitting that next gap up as to what I'm looking for. It currently sort of went in around the sort of 210 mark. Again, maybe strengthen just a little bit just to increase that gap between that and the four hybrid. But we've got plenty of ability to do that. Weight push right at the back. Launches the ball incredibly high. Love the shallow face. That's a personal thing. But if I thought, again, if I was saying to golfers, average golfers out there, the clubs to try, if you try nothing else, it would be this G4, 20, 5 hybrid and fairway range. And then I'd go into a five wood. 17.5 degrees loft, again, does everything. I'm not going to repeat it. So it does everything that the seven wood does with a slightly lower ball flight. But still, again, we were looking at sort of, I reckon we're getting in that around that sort of 215 to 220 mark again. Again, repeating what I'm already saying. Gapping it is very easy to do with that adjustability.  I've already said that. But that is an unreal set of clubs we've got so far. So we've got two to look at. We've got driver and putter, and that leaves us with one spare gap in the bag. Right, so we fought the big reveal in terms of the driver. We're at the bottom end of the bag, and it's the putter. In all honesty, I could have probably picked maybe three, four different options to put in the bag. But for me, this version of the Spyder, the FCG, was particularly impressive. On a personal level, I love the idea of using a blade putter, but my putting style very much suits a mallet. They've got plenty of, and it's kind of, they've almost done a mix of the two. So it's got a blade-like look, almost the white element that you see, but then it's got the supportive elements that you get from a mallet. It gets the ball rolling particularly well. I love the way the putter is balanced. Again, very much a personal and preference thing. And again, a really simple, but strong alignment aid on the front. So for me, the TaylorMade FCG would be the putter of choice. And of course, I love this sort of plumb line neck as well, but that, again, very much a personal choice. So there's only one thing left and that's the driver. Right, so we're into the top end of the bag. I'm still sticking around with the driver and for me, from the 2021 releases, honestly, I could have probably picked any one from about four, but I'm going to go with the Callaway Epic 21. And I'd be stuck to be honest with you, as to whether or not I'd go for the max product or the speed, because I'm really liking both. And there's little to split them. I would carry on doing further testing. At the moment, it's the speed product that I've got in hand and that's the one I'm sort of leaning towards in terms of more aesthetically how it looks and the style of the head, but just as an overall with this Epic range, what they do for me and what I like about them, I love the acoustics from this driver. I think it's fantastic. Love it on the ear. I love it at address. And in terms of out and out performance, it did really well in terms of maintaining ball speed, which I always think that suggests decent forgiveness because I've never gone at this driver consistently out the middle of the face. So it maintained high ball speeds, suggesting forgiveness, and it also did well down range in terms of dispersion. They were incredibly tightly packed. It's different on the range than it is out on the golf course, so we shall see how that would perform in real conditions. But this would certainly be the one that I would choose based on all the testing I've done so far. Closely followed by yet again, I think it would be that Ping G425. So that's me into the top end of the bag. Let's not forget, I've said all along, we'll put a total up now of how much this would cost because it's an expensive set of golf clubs. It really is the best that's out there in my opinion if I was putting the bag together for me now. But you'd need deep, deep pockets. Anyway, as ever, thank you for watching. I think what I'd like to know is what's on your wish list, any of those products, or what are you looking at in particularly this year? Comments down below. Hit that like button and I'll see you very soon. Interesting enough, just to clarify once again, we've been walking around the par three course at the back of four golf. We aren't hitting any golf shots whatsoever before anybody worries if we're breaking any lockdown rules. We're certainly not.


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