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Jérôme April 14, 2004 04:04

Hei, I'm a student, and I'm working on a cfd project. The software computes hydraulics and sediment distribution in a flume. The scheme used is implicit. I'd like to know the way to investigate the stability, especialy concerning the time step. I know the cfl number (courant number), but I don't know really how to use it (good range ...), and if I can apply it to sediment computation. I you have some information or advice, don't hesitate.

The software is SSIIM 3D (from NTNU, Norway)

Jérôme April 14, 2004 07:00

the website of the software :

noName April 14, 2004 11:01

From the website:

"SSIIM is an abbreviation for Sediment Simulation In Intakes with Multiblock option. The program is designed to be used in teaching and research for hydraulic/river/sedimentation engineering. It solves the Navier-Stokes equations using the control volume method with the SIMPLE algorithm and the k-epsilon turbulence model. It also solves the convection-diffusion equation for sediment transport, using van Rijn's formula for the bed boundary. Also, a water quality module is included."

No mention of differencing schemes used? No mention of time marching? Do you know any of these issues?

Ed April 14, 2004 11:33

See "Open Channel Flow" by Dr. Chaudhry for a discussion on the CLF criteria.

Chris April 14, 2004 22:19

Without knowing anything about your software, I do know that for a 1D linear convective equation there is no stability constraint on time-step size. Most of the stability analyses you will find will be for the linear 1D equation. Of course, any real world CFD problem is both non-linear and multi-dimensional so strictly speaking the stability analyses does not hold for these problems.

But there is no analytical method to perform a stability analysis for the Euler or Naver-Stokes equations so most people use the 1D linear convection stability analysis as a starting point and adjust the CFL / timestep based on experiences. Although, if you problems are unsteady time accuracy would need to be considered because stability does not ensure an acceptable level of temporal accuracy.

Most entry level graduate CFD books will explain CFL constraints for the different different algorithms, ie explicit and implicit

Jérôme April 15, 2004 05:25

I have to give more information about the software : The finite volume method is used to discretize Navier Stokes and k-epsilon equation in 3D. For hydraulics computations, a second order implicit upwind scheme is used. Concerning the sediments, the software solves at every time step a continuity equation and a bed load transport formula. You have to enter the time step (it is not link to the space step)

I hope somebody will be able to advice me.

noName April 16, 2004 10:19

"Without knowing anything about your software, I do know that for a 1D linear convective equation there is no stability constraint on time-step size."

Chris, this is what you say above. I might be totally wrong, but don't you need to satisfy a stability criterion in each cell (cell Peclet Number) when solving convection diffusion problems? I think this is one of the first things you notice you program central differencing. So stability is not concerned only with time marching (parbolic part), but also the positiveness (ellipticity) of the M-matrix (tri-diagonal operator).

Chris Sideroff May 16, 2004 14:52

Yes, you are correct it does totally depend on the spatial differencing. I forgot to mention that first-order upwind schemes for 1D linear hyperbolic equations that are unconditionally stable for all CFL numbers.

Central differencing (for 1D linear hyperbolic) is unstable for all CFL numbers, hence the need for artificial dissipation.

This obviously does not hold for multi-dimensional, non-linear systems of equations but in general the CFL condition for implicit schemes are much more relaxed than for explicit schemes - this is why most commercial CFD does employ implicit advancement schemes.]

Sorry for the error.

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