Hi,

I tried to simulate a test case with an initial start of Mach 3 flow. One of the case is the forward step, and another is the Ron-Ho-Ni channel.

When I run my code, after a few iterations, it crashes because of negative pressure value (in the vicinity of wall). In some literatures, it was mentioned that I need to do some entropy correction at the corners/singularity at wall. But, I am just wondering if there is an alternate way to do that. My code is an unstructed WENO type code, with NRBCs as proposed by Lele. For now, I use HLL flux for interfaces.

I tried to lower down the CFL to 0.01... but, still not getting that right...

Can anyone let me know where could I have possibly erred, or missed out? Should I do the entropy correction? and if I should do that, how can I generalize the boundary condition? (Say a Mach 5 problem for Scramjet intake)

(My code works well till Mach 2)

Thanks in advance for your help.

Singularity at the corner of the forward facing step will cause some problems at the shock reflection area on the bottom boundary after the step. You have to cure that singularity in order to have a correct shock reflection. However, I'm not sure if that singularity is the main reason for negative pressure or not. But I'm sure that those negative pressure effects should be cured by local order reduction. That negative pressure arises because you are using a wide stencil for high order accuracy, which can cause problems when two shocks presents together in one stencil. Or may arise while you are trying to reconstruct that high order polynomial where differences of values are very high across a discontinuity (shock) while one part near a zero value. The high order polynomial can drop below zero at those circumstances. Try to use a local order reduction at that point. But as far as I remember from my work for Mach-3 ffs with WENO-5th order with LF flux, there was no need for local order reduction. So there may be another problem with the implementation.

Saygin

Hi Saygin,

Can you let me know whether you did interpolation on the primitive variables or conserved variables or other means? I think I messed up in these...

Thanks for your help!

DSS

Hi Saygin,

I figured out the error... I made a goof up when I transited my code from interpolating the conserved variables to interpolating the primitive variables. I missed out a division by density in the energy term. Now, the boundary condition works fine. But, am still curious... I read in literature that one should use charateristic variables in interpolation for improved order of accuracy. Did you try those?

DSS

Hi DSS,

I used conservative variables for reconstruction/interpolation. Do you mean using characteristic space by the "characteristic variables"? If you mean that, yes it is correct. Component-wise decompositions are cheaper to implement and to run but gives oscillations and it is not prefered and I don't prefer also. Using characteristic-wise decomposition is costly compared to component-wise but gives non-oscillatory and elegant results. So in summary what I did was; after a Roe-averaging (for linearization -freezing the variables-) projecting the conservative variables to the characteristic space (by that way the vectors are decoupled), applying reconstructions there, and then projecting back to the physical space.

Saygin