# Time Stepping

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 September 4, 2002, 18:03 Time Stepping #1 Chan K I Guest   Posts: n/a Sponsored Links Hi, 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

 September 5, 2002, 02:05 Re: Time Stepping #2 Tom Guest   Posts: n/a 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

 September 5, 2002, 11:22 Re: Time Stepping #3 Chan K I Guest   Posts: n/a Hi Tom, Thanks for your reply. The scheme has been well-assessed beforehand and is being implemented on an internal flow case.

 September 6, 2002, 16:07 Re: Time Stepping #4 Pao Guest   Posts: n/a Are you running the transient solution? or steady state solution?

 September 6, 2002, 17:30 Re: Time Stepping #5 Chan K I Guest   Posts: n/a 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

 September 6, 2002, 17:36 Re: Time Stepping #6 Pao Guest   Posts: n/a But after a long iteration, the steady state solution is independent from the time step. This is my experience.

 September 7, 2002, 04:50 Re: Time Stepping #7 versi Guest   Posts: n/a 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.

 September 7, 2002, 09:51 Re: Time Stepping #8 Jim Park Guest   Posts: n/a 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.

 September 8, 2002, 14:43 Re: Time Stepping #9 Chan K I Guest   Posts: n/a 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? Cheers

 September 9, 2002, 10:44 Re: Time Stepping #10 Pao Guest   Posts: n/a How about the external flow calculation? Did you see time step affect the solution? Or this only happen for internal flow problem?

 September 10, 2002, 10:05 Re: Time Stepping #11 Chan K I Guest   Posts: n/a 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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