Monday, January 11, 2010

Steady versus Unsteady Flow

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I was recently emailed this question regarding steady flow versus unsteady flow results:

“My question is fairly basic. I have heard from a couple of other engineers that when flood levels are generated with usteady flows that it is typical to then run a steady simulation with the routed flows from the unsteady run as unsteady results may be considered less accurate? Is this standard or conventional practice to your knowledge? “

While it is common to have a companion steady flow version, I would disagree that this is done because unsteady results are considered less accurate. Two equally well constructed models, one steady, one unsteady could certainly produce different results, but the unsteady will be more accurate. The unsteady flow St. Venant equations are more physically correct than the energy equation which is used to compute steady flow. From a numerical standpoint, the energy equation has an advantage in that it can be analytically solved, yielding an exact solution. The unsteady flow equations must be reduced to a discrete form (finite difference approximation) to solve, so there is some built-in error. However, if done correctly, this error is inconsequential for river models. RAS does a good job of this. The biggest difference is that steady flow models do not take into account the effects of in-channel and off-line storage in the attenuation of the flood wave. This can be quite significant. Some modelers take the tact of constructing a steady flow model with the computed routed flows from the unsteady flow model. While this is a “forced” way of accounting for the storage effect, it is no more accurate than its unsteady counterpart. And it would be a significant effort to set up a steady flow model with a flow change at every cross section. I don’t recommend it.

In short, given two equally well constructed models, one steady and one unsteady, of the same reach, I would take the results from the unsteady flow model every time.

Any other thoughts out there on this subject?


  1. One reason I've heard is that the floodway methodology doesn't work the same way in unsteady mode. Using this method should allow one to construct the unsteady model to handle the routing of the flood wave, then take the peak flows and use them for floodplain mapping and floodway definition.

    Also, the water surface elevations reached using this method should be somewhat higher than the unsteady results, as they are using peak-on-peak flow values. That would be seen as a conservative estimate of water surface elevation.

    I'm not sure I like the method, but these are the reasons I've heard.

  2. You have a good point in your post. May I know your source for those ideas so that I could cite it in my document?

  3. I can't give you a single source. A lot comes from my own study and research. The RAS manuals discuss a lot of this, as would any graduate level textbook that covers unsteady open channel flow hydraulics. You are welcome to reference this blog post if you'd like.