[usv001]

Dear all,

I am trying to run the double Mach reflection case using WENO schemes. When I tried using component-wise WENO5 with HLL flux, I obtained the result shown in the attached image. The domain is 3.25 m x 1.0 m and the mesh resolution is .

I have a couple of questions regarding the result:

• Why do the oscillations appear next to the shocks? Are they related to the flux scheme or WENO reconstruction? What can I do to get rid of them?
• What is the other streak that emanates from the top boundary where the shock intersects it? I have used a codedFixedValue boundary condition at the top to follow the shock at the exact speed but the streak still appears. Is it expected? How to eliminate it?

Any reply/suggestion would be helpful to me.

With many thanks,
USV

[OlegSutyrin]

Hi, usv001!
I'm currently struggling with WENO methods too :-)
As for you questions, I think (I'm not a specialist, these are my guesses!) that:
1. Oscillations may be generated by the fact that component-wise WENO does not upwind fluxes correctly. You should try characteristic-wise method, i.e. transform your variables to characteristic field before applying WENO reconstruction. My questions - one and two - at stackexchange may help you.
2. I often see such weak "garbage" when set initial conditions for shock as sharp jump (something like micro-Riemann problem happens there before shock is properly smeared by the numerical method). Maybe you have something similar here, caused by "sharpness" of boundary conditions?

P.s. Why this thread is in OpenFOAM subforum? AFAIK, OpenFOAM does not support WENO methods...

[usv001]

Hi Oleg,

Thank you for your reply. I managed to implement a characteristic-based WENO method. I followed the implementation suggested in this paper. It has solved the problem of oscillations next to the shock inside the bubble (see the attached results).

As for the streak emanating from the top boundary, it still remains unsolved. I agree with you that it is probably due to the sharpness of the boundary condition; the shock has not been not allowed to smear to its viscous profile. So, I guess the question is how do you initialize and set the boundary conditions to obtain a good solution to this problem?

As for why this thread is under OpenFOAM, I just happen to develop these methods in OpenFOAM.

USV

[OlegSutyrin]

Originally Posted by usv001

Hi Oleg,

Thank you for your reply. I managed to implement a characteristic-based WENO method. I followed the implementation suggested in this paper. It has solved the problem of oscillations next to the shock inside the bubble (see the attached results).

Great! I'm happy that I was right :-)

Originally Posted by usv001

As for the streak emanating from the top boundary, it still remains unsolved. I agree with you that it is probably due to the sharpness of the boundary condition; the shock has not been not allowed to smear to its viscous profile. So, I guess the question is how do you initialize and set the boundary conditions to obtain a good solution to this problem?

In my finite-difference programs, I usually copy field values from inside the computational area to the boundary (simple "non-reflecting" condition) with regard of geometry of course. For your problem I would try to transfer values from almost-top grid point to the topmost ones along the shock front. I'm not sure what to do with finite-volume methods though...

Originally Posted by usv001

As for why this thread is under OpenFOAM, I just happen to develop these methods in OpenFOAM.

Whoa! AFAIK, WENO are mainstream modern methods for gas dynamics, it would be very good to have them in OpenFOAM. It is important task, good luck with it!