[freefem]

Hello everyone,

Recently, I met problems in implementing a solver for standard double mach reflection. My problem is that when I use component wise reconstruction, in some cells, the pressure will be negative. I wonder if it has something to do characteristic decomposition? If so, how can I do characteristic decomposition in 2D?

(I use WENO5-LF to solve smooth problems and has verified that the solution is of order 5. So I think the other part is most likely correct.)

Thanks a lot.

[usv001]

Hi there,

I am having similar problems with component-wise WENO7 - the simulation crashes every time (most likely due to negative pressure or energy). However, with component-wise WENO5 I was able to run the case.

Also, I have coded a dimensionally-split characteristic decomposition and validated it for some 1D and 2D cases. However, it crashes for both WENO5 and WENO7 for the double Mach reflection.

I'd like to know if you've managed to solve your problem and, if so, could you please share your solution?

Many thanks,
USV

[mczero57]

Hi freefem,

If I recall correctly, this is a M=10 problem of a moving shock impinging on a wall. I am assuming you are reconstructing the conserved variables. What most people do is this : Over the whole stencil of cells, a transformation is made to the local characteristic variables. This transformation matrix is a constant matrix. The WENO5-Lax-Friedrichs reconstruction is performed on these transformed variables. Once the reconstructed values are obtained at the cell faces, the inverse transformation is used to evaluate the fluxes.

The key is that this transformation is a constant matrix - what is it ? The common choice is to use the transformation matrix frozen at the average of the left and right values of the cell averages of that face. For more details, you should refer to the paper by Harten, Osher and Chkravarthy.

Hope that helps
Sam

Originally Posted by freefem

Hello everyone,

Recently, I met problems in implementing a solver for standard double mach reflection. My problem is that when I use component wise reconstruction, in some cells, the pressure will be negative. I wonder if it has something to do characteristic decomposition? If so, how can I do characteristic decomposition in 2D?

(I use WENO5-LF to solve smooth problems and has verified that the solution is of order 5. So I think the other part is most likely correct.)

Thanks a lot.