Time Stepping
Hi,
I am a running an internal flow timemarching simulation using Jameson's RungeKutta scheme. At different CFL numbers, the converged solution is different. Any ideas what could be the problem? Thanks very much Chan K I 
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.
Tom 
Re: Time Stepping
Hi Tom,
Thanks for your reply. The scheme has been wellassessed beforehand and is being implemented on an internal flow case. 
Re: Time Stepping
Are you running the transient solution? or steady state solution?

Re: Time Stepping
Hi Pao,
I am running a timemarching solution to a steadystate. Noticed that with same initial conditions, different time steps give different steadystate solutions. Thanks very much 
Re: Time Stepping
But after a long iteration, the steady state solution is independent from the time step. This is my experience.

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 0vortex, 1vortex and 3vortex flows at the same Re number. Please specify your flow problem in detail.

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. 
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 timemarching 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? Cheers 
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?

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