Dear friends, I wrote a code to solve 3D Euler equations(finite volume method, unstructured,roe scheme). I works well for transonic flow and supersonic flow with Mach less than 2.0. For hypersonic flow, the code breaks down because some value turns negative under squareroot. Could you give me some help? Thanks.

If your code is no problem, it's mostly like initial condition problem. You may try to use low mach number solution as initial condition for high mach number or simply set a positive value if you solver is robust enough. But you have to check and make sure this negative value will disappear when convergence solution is reached. Good luck!

Have you ever used entropy fix?If so,try another one because the entropy fix is problem dependent.The paper concened can be found on the J.C.P 1998;If not,add the entropy fix to your code because Roe scheme needs entropy fix to circumvent the occured unstability.

Good luck to you!

This is due to high CFL number..u might reduce the time step..this will yield converged solution..hope you good luck..

It is most likely due to oscilations in your solution. At higher Mach number, the pressure ratio (Ps/Pt) is getting smaller and smaller. (For example, at M=2.5, Ps/Pt=0.0585). If there is an oscilation in your solution(say, at the shock waves, or sudden expension), this small number can easily drops to a negative value. In most case, you may have either a negative Pressure or negative Density, or both. This is particularly common at hypersonic flows with strong shock waves.

Here are some suggestions: (1) Check your solutions at low Mach to see if there is any oscilations near shock waves and other contact discontinuity. This oscilation may not turn the pressure and density to negative values because the pressure ration is still high enough.

(2) If there is oscilations at low Mach number, work with the algorithm to remove the oscilation. (by the way, which Roe scheme did you use?)

(3) If there is NO oscilation in your final steady state solution, there must be oscilations during your 'starting' period. You may use 'slow start' method by using small CFL number at the beginning, and gradually increase it to its normal value. In the mean time, use some 'foolish' methods to get rid of the nonsense values at this transition period (for example. if Ps<0.0001, then set Ps=0.0001, (Mach=8.0), if need higher Mach, set even smaller value). When the transition starting period is over, the code (if there is no build-in oscilation) should happly converges to the solution.

Best wishes.

Hongjun

I think there are two possibilities: one is the scheme need a limiter(I used the method of Dr. Neal Frink and there is no limiter); the other is the roe scheme needs a entropy fix(or other fix).

Hi,

I know what the problem is. I have computed both supersonic and hypersonic high speed flows around cylinders and flares.

The critical issue is regarding Entropy fixes.

1) The Entropic fixes at high Mach numbers is

to added for all waves irrespective of which

eigen valus u+c, u, u-c vanishes

2) Make sure that the u wave (Shear) also has a fix

beacause if your flow is grid alligned then the

normal component to the flow is zero and this will lead to severe oscillatiions as mentioned by one of the researchers.

3) The Entropy fix should be related to the spectral radius |u| + c and is usually higher for hypersonic flows. I have a paper on this in AIAA. (1994).

4) non-dimentionalize the velocities for the fix as Harten-Yee do with the accoustic speed as the non-dimensionalization parameter.

Ravi Krishnamurthy

Dear Krishnamurthy, Thank you for your help! Could you tell me the number of AIAA paper you mensioned?