I am using a Non-dimensional Euler code to simulate a shock wave passing over an obstacle. When the post shock flow is almost sonic, the 'vortex' generated by the flow is such that after some elapse time, the non-dimensional density goes to zero and the entire solution blows up. Changing it to a viscous code will eliminate the problem but will also erase alot of shock structures in the flow.

I am wondering what is the reason for this phenomenon? Non-dimensionalising? And is there anyway to overcome this problem other than by using artificial dissipation or a viscous code?

Thanks Yibin

Non-dimensionalizing is a good way to obtain universal solution and scale variables to O(1) ranges. It has nothing to do with solution divergence. The reason may be there are significant numerical oscillations in the subsonic region after the shock wave. You can first increase the artificial viscosity to see if the solution still overflows, or can later adopt other schemes like TVD type with entropy correction for strong shock over obstacles like blunt body.

That's what I understand from non-dimensionalizing.

But I don't think the solution blowing up is due to solution divergence as the solution are resonable except the pressure, density of the centre of the vortex keeps dropping, and due to my calculation of the flux terms, e.g. u vel from rho*uvel/rho term, once the density hits zero the entire solution became NaN. It is abrupt in that sense.

I am using Visbal's filtering method, a 'sort' of artificial dissipation, to keep numerical oscillations down, and it is working quite well for a simple shock tube problem and even for flow over a blunt body for lower shockwave mach number.

For my code, I am using a DRP scheme on a structured mesh for spatial discretization and a traditional 4RK scheme for time marching.