artifcats in an radialy expending flow
 

Hi,

I am trying to model the 2D shock between two compressible hypersonic flows. one of my two flows is expending radialy form a source placed in the middle of my space domain. I am using an Upwind-Lax-Friedrich scheme to resolve my Euler's equations, with an cartesian structured grid.

I have a problem in modeling the radial expansion of my first flow. The circular source is discretised using 32*32 cells. When my flow start to radially expend from the source, artifacts occurs showing anomalies between the grid aligned direction and the diagonal directions.

I saw that the major part of works done on that subject (expanding flow or detonation) use curviliniar mesh more appropriate to treat radial expansion.

Infortunatly I need to use my cartesian grid. Is there any solution to minimize the effect of these artifacts (other than using an extreme level of refinement near the source).

Thank you in advance

Mehdi

Re: artifcats in an radialy expending flow
 

Upwind-Lax-Friedrich (1st order) is very dissipative, can not be reliable. You can choose other 2nd scheme, like MUSCL-Roe, TVD, ENO. Gundnov. Also there is a problem of boundary well posedness for source flow.

Re: artifcats in an radialy expending flow
 

I am assuming you are using a finite volume method. In that case are you taking cell-averages for initial condition ? The cell-average contains more information about initial discontinuity and is absolutely essential to get correct solution.

Re: artifcats in an radialy expending flow
 

Hi,

Thank you for you advance, I am just identifing the problem : I am using for my reconstruction a limiter based on albada formula. In this limiter I use only the four surrounding neighbors (I am in 2-D) to compute the forward and the backward diffrence operator and to extrapolate form there to the the face values.

I tried a Minmod limiter that include the corner cells amd it working pretty good. My artifacts completly disapeared for the diagonal moving flow.

The Question That rise now is how to take account of the corner cells in the classic interpollation scheme using the forward and the backward difference ?

Mehdi