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Bigarella August 7, 2002 21:54

CFL limits for separated flow

I'm working on a finite difference method for aerospace applications. This is a 2-D (actually 3-D, but think 2-D for this problem), explicit, centred-difference method, that solves the compressible RANS plus eddy viscosity turbulence models (SA, SST). I use a 5-stage, 2-nd order Runge-Kutta for time stepping, plus implicit residual smoothing and multigrid. The limiting CFL number for this RK is 2*SQRT(2), but the residual smoothing allows for CFL = 4 for some of my aplications.

The flows I'm interested in have Mach numbers of M=0.9 to 3.0 and Reynolds number of about 9 million to 30 million. The rocket geometry I work at is something like this monster:


/ \junction_____ --> air speed ( _____________|<


(obviously not so rough) =D

The problem I'm facing is that, for some conditions, the flow separates in the junction of the payload fairing and the lower-diameter cylinder, and this separation forms a little bubble there. My code, however, blows at it. I would like to know which possible reasons could be generating it? Some options:

1. High CFL number? It is currently CFL = 4. Is it to high for a Runge-Kutta scheme with separated flow? 2. The multigrid? Does it handle well separated flows? 3. Should I throw it all away and go to the beach? ;)

Thanks in advance, Biga

Li Yang August 8, 2002 10:57

Re: CFL limits for separated flow

I have got the impression that the central difference scheme can only be used for a Mach number up to 1.1 or 1.2. Above that it fails.


Bigarella August 8, 2002 11:01

Re: CFL limits for separated flow
Thanks for your reply.

I don't think so! I have very good results for Mach=4, it depends on the quality of your artificial dissipation scheme.

Li Yang August 11, 2002 07:22

Re: CFL limits for separated flow
It is very interesting to know that central difference scheme can perform well at Mach=4. How is the shock position has been predicted in your calculation ? Does the artificial viscosity need to be specially specified for such a high Mach number ? I thought that only upwind schemes such as Roe's scheme can capture the shock position precisely for strong shock problem.

I would suggest you to use a smaller CFL number to start with. To my knowledge, even for an implicit scheme, a solver may not work with a large CFL number for a specific flow.



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