Boundary Condition of Shock Waves Interaction Experiment
 

Dear Sir or Madam:

Hello!
I am a graduate student in Math department, recently I am doing a project about shock waves interaction.
I have a question about shock wave interaction, which confused me for a long time.:confused::confused::confused: Please find the slides attached.

We designed an experiment to make two shocks encounter in the middle area, the Lax-Wendroff scheme was used to get the finally updated flow filed. Even though the incident shocks and part of their reflected shocks can captured clearly, all the parameters get dramatically high in the middle area.

More important, I expect the results which are similar with the theory results, you can find the theory shock wave interaction result in the end of that slides.

We think this bad result was caused by the boundary conditions in the output area(or the upper boundary in the middle), and I could not find a good way to fix it.
Could you please give me some comments or suggestions about this problems? I would appreciate if you can help me.

Best Wishes and Kind Regards,
Sun Ligang

I have not read the pdf but, before checking the BC.s, have you experience of CFD? Do you know that the Taylor expansion (on which the L-W is based) is not valid where a discontinuity of the functions is present? The L-W scheme can be used for the weak form and you should deduce the numerical flux function.
In any case, such scheme produces numerical oscillation, can be entropy violating. In conclusion, start using a simple first order method to check first if the BC.s are correct. Then, if the solution is physically relevant (even if smooth for the numerical visosity) you can try to improve the accuracy.

Hello, FMDenaro:

Many thanks for your reply!!
I just submitted my second experiment, i.e., the interaction experiment with some problems. For the first reflection experiment, the result is very good, please see the new attachments. Both these two experiments are based on 2D Lax-Wendroff method. So I just consider if the boundary conditions caused the terrible results. It is really strange for the reflected shock just gets very high in the middle area.

I am a graduate in Math department, I have only a little experience in CFD. But my friend had. He got a PhD in Flow Mechanics, but he still could not fix this.

Thank you and I am looking forward to your reply!

Kind Regards,
Sun Ligang

It is quite easy to check if the BC.s introduce spurious waves... "non-reflecting boundary conditions" is a very old and well documented issue in the CFD literature (textbooks and journals). I suggest to check your code in a well known test-case, then you should control the field during the time integration to see what happen when the waves move close to the boundary

May i suggest to first try some 1D experiments (shock tube) both aligned and not with respect to your grid? In this way you can quickly rule out some possible issues. I would first focus on the solver (using simple b.c.s) and then on the b.c.s (using a simpler problem). I expect something to show up before you complete the whole set of experiments.

Also, as Prof. Denaro wrote, testing the 1st order is somehow mandatory before the more complex schemes. You might be just looking at some feature of the scheme without even knowing it.

Most of these tests are long/boring but, there is no actual alternative.

Yes, it is long tests. Actually even the one moment flow field information would cost more than 3 hours to achieve, and the txt file which was used to store the data is about 50M.
Many thanks for your suggestions! I am going to check that.

Thank you for you suggestions, Dr. Denaro!
I am going to check the code again, and I will submit the new output and let you know.
Thanks!