{"action":"created","comment":{"url":"https://api.github.com/repos/geodynamics/aspect/pulls/comments/47149232","id":47149232,"diff_hunk":"@@ -6310,11 +6315,78 @@ \\subsubsection{The van Keken thermochemical composition benchmark}\n parameter (the division by 0.02 in the formula for the smoothed initial\n condition). However, for more exact results, one can choose\n this half width parameter proportional to the mesh size and thereby get more\n-accurate results. Since the point of the section was to demonstrate the reason\n-for the lack of convergence, but we leave this as an experiment to the reader.\n+accurate results. The point of the section was to demonstrate the reason\n+for the lack of convergence.\n \n+In this section we extend the van Keken cookbook following up the work previously completed by Cedric Thieulot, Juliane Dannberg,\n+Timo Heister and Wolfgang Bangerth.  \\textit{This section contributed by Grant Euen, Tahiry Rajaonarison, and Shangxin Liu as part of the Geodynamics and ASPECT class at Virginia Tech.}  \n \n+As already mentioned above, using a half width parameter proportional to the mesh size allows for more accurate results.  We test the effect of the half width size of the smoothed discontinuity by changing the division by 0.02, the smoothing parameter, in the formula for the smoothed initial conditions into values proportional to the mesh size.  We use 7 global refinements because the root mean square velocity converges at greater resolution while keeping average runtime around 5 to 25 minutes.  These runtimes were produced by the BlueRidge cluster of the Advanced Research Computing (ARC) program at Virginia Tech.  BlueRidge is a 408-node Cray CS-300 cluster; each node outfitted with two octa-core Intel Sandy Bridge CPUs and 64 GB of memory.  A chart of average runtimes for 5 through 10 global refinements on one node can be seen in Table~\\ref{tab:runtime-table}.  For 7 global refinements (128$\\times$128 mesh size), the size of the mesh is 0.0078 corresponding to a half width parameter of 0.0039.  The smooth model allows for much better convergence of the secondary plumes, although they are still more scattered than the primary plumes.\n \n+\\begin{table}[htb]\n+\t\\center\n+\t\\begin{tabular}{|c|ccccc|}\n+\t\t\\hline\n+\t\tGlobal & \\multicolumn{4}{|c|}{Number of Processors} \\\\\n+\t\tRefinements & 4 & 8 & 12 & 16\n+\t\t\\\\ \\hline\n+\t\t5 & 28.1 seconds & 19.8 seconds & 19.6 seconds & 17.1 seconds \\\\\n+\t\t6 & 3.07 minutes & 1.95 minutes & 1.49 minutes & 1.21 minutes \\\\\n+\t\t7 & 23.33 minutes & 13.92 minutes & 9.87 minutes & 7.33 minutes \\\\\n+\t\t8 & 3.08 hours & 1.83 hours & 1.30 hours & 56.33 minutes \\\\\n+\t\t9 & 1.03 days & 15.39 hours & 10.44 hours & 7.53 hours \\\\\n+\t\t10 & More than 6 days & More than 6 days & 3.39 days & 2.56 days \\\\ \\hline\n+\t\\end{tabular}\n+\t\\caption{\\it Average runtimes for the van Keken Benchmark with smoothed initial conditions.  These times are for the entire computation, a final time step number of 2000.  All of these tests were run using ASPECT version 1.3 in release mode, and used different numbers of processors on one node on the BlueRidge cluster of ARC at Virginia Tech.}\n+\t\\label{tab:runtime-table}\n+\\end{table}\n+\n+This convergence is due to changing the smoothing parameter, which controls how much of the problem is smoothed over.  As the parameter is increased, the smoothed boundary grows and vice versa.  As the smoothed boundary shrinks it becomes sharper until the original discontinuous behavior is revealed.  As it grows, the two layers eventually become one large, transitioning layer rather than two distinct layers separated by a boundary.  These effects can be seen in Fig.~\\ref{fig:vk-5}.  The overall effect is that the secondary rise is at different times based on these conditions.  In general, as the smoothing parameter is decreased, the smoothed boundary shrinks and the plumes rise more quickly.  As it is increased, the boundary grows and the plumes rise more slowly.  This trend can be used to force a more accurate convergence from the secondary plumes.\n+\n+\\begin{figure}\n+\t\\centering\n+\t\\includegraphics[width=0.8\\textwidth]{cookbooks/benchmarks/van-keken/smoothing-parameter.png}\n+\t\\caption{\\it Van Keken Benchmark using smoothed out interface at 7 global refinements: compositional field at time $t=0$ using smoothing parameter size: a) 0.0039, b) 0.0078, c) 0.0156, d) 0.0234, e) 0.0312, f) 0.0390, g) 0.0468, h) 0.0546, i) 0.0624.}\n+\t\\label{fig:vk-5}\n+\\end{figure}\n+\n+The evolution in time of the resulting compositional fields (Fig.~\\ref{fig:vk-6}) shows that the first peak converges as the smoothed interface decreases. There is a good agreement for the first peak for all smoothing parameters.  As the width of the discontinuity increases, the second peak rises both later and more slowly.\n+\n+\\begin{figure}\n+\t\\centering\n+\t\\includegraphics[width=0.75\\textwidth]{cookbooks/benchmarks/van-keken/smoothing-parameter-velocity.png}\n+\t\\caption{\\it Van Keken benchmark with smoothed initial conditions for the compositional field using 7 global refinements for different smoothing parameters.  Number of time steps is shown on the x-axis, while root mean square velocity is shown on the y-axis.}","path":"doc/manual/manual.tex","position":82,"original_position":82,"commit_id":"8304f22af8f3c2402dd75e783dc06d129079c712","original_commit_id":"8304f22af8f3c2402dd75e783dc06d129079c712","user":{"login":"bangerth","id":7504421,"avatar_url":"https://avatars.githubusercontent.com/u/7504421?v=3","gravatar_id":"","url":"https://api.github.com/users/bangerth","html_url":"https://github.com/bangerth","followers_url":"https://api.github.com/users/bangerth/followers","following_url":"https://api.github.com/users/bangerth/following{/other_user}","gists_url":"https://api.github.com/users/bangerth/gists{/gist_id}","starred_url":"https://api.github.com/users/bangerth/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/bangerth/subscriptions","organizations_url":"https://api.github.com/users/bangerth/orgs","repos_url":"https://api.github.com/users/bangerth/repos","events_url":"https://api.github.com/users/bangerth/events{/privacy}","received_events_url":"https://api.github.com/users/bangerth/received_events","type":"User","site_admin":false},"body":"Please write it as `$x$-axis` and same for 'y'.\r\n\r\nI think the correct term for the x-axis would be \"Number of the time step is shown...\"","created_at":"2015-12-09T20:46:47Z","updated_at":"2015-12-09T20:46:47Z","html_url":"https://github.com/geodynamics/aspect/pull/683#discussion_r47149232","pull_request_url":"https://api.github.com/repos/geodynamics/aspect/pulls/683","_links":{"self":{"href":"https://api.github.com/repos/geodynamics/aspect/pulls/comments/47149232"},"html":{"href":"https://github.com/geodynamics/aspect/pull/683#discussion_r47149232"},"pull_request":{"href":"https://api.github.com/repos/geodynamics/aspect/pulls/683"}}},"pull_request":{"url":"https://api.github.com/repos/geodynamics/aspect/pulls/683","id":52922228,"html_url":"https://github.com/geodynamics/aspect/pull/683","diff_url":"https://github.com/geodynamics/aspect/pull/683.diff","patch_url":"https://github.com/geodynamics/aspect/pull/683.patch","issue_url":"https://api.github.com/repos/geodynamics/aspect/issues/683","number":683,"state":"open","locked":false,"title":"Cookbook ex","user":{"login":"GEuen","id":15220270,"avatar_url":"https://avatars.githubusercontent.com/u/15220270?v=3","gravatar_id":"","url":"https://api.github.com/users/GEuen","html_url":"https://github.com/GEuen","followers_url":"https://api.github.com/users/GEuen/followers","following_url":"https://api.github.com/users/GEuen/following{/other_user}","gists_url":"https://api.github.com/users/GEuen/gists{/gist_id}","starred_url":"https://api.github.com/users/GEuen/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/GEuen/subscriptions","organizations_url":"https://api.github.com/users/GEuen/orgs","repos_url":"https://api.github.com/users/GEuen/repos","events_url":"https://api.github.com/users/GEuen/events{/privacy}","received_events_url":"https://api.github.com/users/GEuen/received_events","type":"User","site_admin":false},"body":"This request submitted by the Geodynamics and ASPECT class at Virginia Tech. The students involved are Grant Euen, Tahiry Rajaonarison, and Shangxin Liu. We updated the Van Keken benchmark cookbook looking at the smoothing parameter for the case 1a isoviscous Rayleigh-Taylor instability.  We also added cases 1b and 1c, nonisoviscous Rayleigh-Taylor instability using both discontinuous and smooth interfaces between layers (Van Keken et al., 1997).","created_at":"2015-12-08T00:28:20Z","updated_at":"2015-12-09T20:46:48Z","closed_at":null,"merged_at":null,"merge_commit_sha":"3f9e312ec7c2f0b8d066279190d2bdbced60a8cd","assignee":null,"milestone":null,"commits_url":"https://api.github.com/repos/geodynamics/aspect/pulls/683/commits","review_comments_url":"https://api.github.com/repos/geodynamics/aspect/pulls/683/comments","review_comment_url":"https://api.github.com/repos/geodynamics/aspect/pulls/comments{/number}","comments_url":"https://api.github.com/repos/geodynamics/aspect/issues/683/comments","statuses_url":"https://api.github.com/repos/geodynamics/aspect/statuses/8304f22af8f3c2402dd75e783dc06d129079c712","head":{"label":"GEuen:cookbook_ex","ref":"cookbook_ex","sha":"8304f22af8f3c2402dd75e783dc06d129079c712","user":{"login":"GEuen","id":15220270,"avatar_url":"https://avatars.githubusercontent.com/u/15220270?v=3","gravatar_id":"","url":"https://api.github.com/users/GEuen","html_url":"https://github.com/GEuen","followers_url":"https://api.github.com/users/GEuen/followers","following_url":"https://api.github.com/users/GEuen/following{/other_user}","gists_url":"https://api.github.com/users/GEuen/gists{/gist_id}","starred_url":"https://api.github.com/users/GEuen/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/GEuen/subscriptions","organizations_url":"https://api.github.com/users/GEuen/orgs","repos_url":"https://api.github.com/users/GEuen/repos","events_url":"https://api.github.com/users/GEuen/events{/privacy}","received_events_url":"https://api.github.com/users/GEuen/received_events","type":"User","site_admin":false},"repo":{"id":44762174,"name":"aspect","full_name":"GEuen/aspect","owner":{"login":"GEuen","id":15220270,"avatar_url":"https://avatars.githubusercontent.com/u/15220270?v=3","gravatar_id":"","url":"https://api.github.com/users/GEuen","html_url":"https://github.com/GEuen","followers_url":"https://api.github.com/users/GEuen/followers","following_url":"https://api.github.com/users/GEuen/following{/other_user}","gists_url":"https://api.github.com/users/GEuen/gists{/gist_id}","starred_url":"https://api.github.com/users/GEuen/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/GEuen/subscriptions","organizations_url":"https://api.github.com/users/GEuen/orgs","repos_url":"https://api.github.com/users/GEuen/repos","events_url":"https://api.github.com/users/GEuen/events{/privacy}","received_events_url":"https://api.github.com/users/GEuen/received_events","type":"User","site_admin":false},"private":false,"html_url":"https://github.com/GEuen/aspect","description":"A 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