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Chan K I September 4, 2002 18:03

Time Stepping

I am a running an internal flow time-marching simulation using Jameson's Runge-Kutta scheme.

At different CFL numbers, the converged solution is different. Any ideas what could be the problem?

Thanks very much Chan K I

Tom September 5, 2002 02:05

Re: Time Stepping
You are sure that the implimentation of the Jameson scheme is correct? Perhaps you can test your code with a well defined (laminar) problem.


Chan K I September 5, 2002 11:22

Re: Time Stepping
Hi Tom,

Thanks for your reply.

The scheme has been well-assessed beforehand and is being implemented on an internal flow case.

Pao September 6, 2002 16:07

Re: Time Stepping
Are you running the transient solution? or steady state solution?

Chan K I September 6, 2002 17:30

Re: Time Stepping
Hi Pao,

I am running a time-marching solution to a steady-state.

Noticed that with same initial conditions, different time steps give different steady-state solutions.

Thanks very much

Pao September 6, 2002 17:36

Re: Time Stepping
But after a long iteration, the steady state solution is independent from the time step. This is my experience.

versi September 7, 2002 04:50

Re: Time Stepping
You may encouter MULTIPLE solutions for an encolsed region, if Re is high enough. This is physically possible. For example, Spherical Coutte flow may have 0-vortex, 1-vortex and 3-vortex flows at the same Re number. Please specify your flow problem in detail.

Jim Park September 7, 2002 09:51

Re: Time Stepping
As early as 1972, Pat Roache published a study showing multiple (steady state) numerical solutions for the same physical problem as he changed the time step.

Try Roache, Patrick J., "On Artificial Viscosity," Journal of Computational Physics, Vol 10, No. 2, October, 1972.

Chan K I September 8, 2002 14:43

Re: Time Stepping
Hi guys,

Thanks so much for your comments!

Pao: The small time step calculation has been run for a reeally long time and the observed trend for mass flow (this is an internal flow problem) shows it converges to a smaller value than for the large time step case.

Versi: This is a time-marching solution to the compressible Euler equations. Hence Re can be taken to be infinity.

Jim: Am going to browse through the paper.

Any more ideas out there?


Pao September 9, 2002 10:44

Re: Time Stepping
How about the external flow calculation? Did you see time step affect the solution? Or this only happen for internal flow problem?

Chan K I September 10, 2002 10:05

Re: Time Stepping
The code was developed for internal flow cases. Previous internal flow simulations did not yield the problem. Only encountered it recently.


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