Hi,

I am trying to simulate a 2-D the expension of a gas released in the vaccum form a spherical source. To do that, I am using the TVD lax-freidrich method with a second-order MUSCL reconstruction to solve the Euler equations. I am using also an Adaptive Mesh with a very high resolution near the source, and going lower as I go far form the source. My gas is modeled by the rho, u, v, and p primitive variables.

Normaly the solution need to be in r^-2 for the density and in log(r) for the velocity norm. The velocity is starting around mach 2 and increase very quickly as the gas is cooling.

I have trouble in getting the desired solution. In fact my velocity solution is not radial as it should be. I found that the flux moving on the mesh main directions has lower velocity that the one moving on the grid diagonals, giving me a star pattern (it is like having jets). And it gives me a star pattern for the density and the pressure too.

I tried many things : higher order scheme, correct the coarse solution at the refinement jump with the finer solution fluxes, interpolate and restrict the conservative variables and not the primitive variables ...etc. Nothings seems to work.

If any body has any idea about the subject, I will be very glad to send you some figures showing the problems and discuss the problem togother. Your help will be appreciated.

Regards

Mehdi

Are you solving time accurate (transient) or do you use a local timestep?

Hi Brat,

I am using a local timestep ! I have more than 20 level of refinement so I can't really use the time accurate scheme. And since I am only looking for a steady state solution, the local time stepping is convienent.

I was discussing with a collegue who told me that maybe I should check about the V scheme for multigrid.

Until now I just solve the equations in all the cells with a local time stepping (I have block structures with 16 central cells for each block with also 2 extra lines and rows of guradcells coming form the neighbors). After that I interpolate the solution from coarse to fine blocks and I restrite it from fine to coarse blocks to be able to fill the blocks guardcells. And I move to the next time step, and so on.

so What I am suppose to do with a V scheme ? Do you think that it is the source of my probleme ?

Regards