Riemann Solvers in multidimension
 

Hi,

Given two state vectors at left and right side of the face, can anyone explain me how to proceed with the Riemann Solvers? In case of cartesian mesh, I guess it is straight forward to treat it dimension by dimension.

But, when the face normal is not aligned with the axis, should we do a coordinate transform for the state vectors? How do we calculate the left and right wave speeds?

I am a bit confused becasue, the HLLC solver works for cartesian coordinates, but, fails with unstructed grid. If I use a simple averaging, it works fine. So, I am sure I have some error in implementation of the Riemann solver.

Thanks in advance for your help.

Re: Riemann Solvers in multidimension
 

Any Riemann solver can be used for unstructured grids. The Riemann problem is considered as taking place in the direction normal to the cell face. Use the cell quantities (with higher-order interpolation if desired) to construct the left and right states. The flux passing through the face is then determined. Just construct a local coordinate system at the cell face.

Re: Riemann Solvers in multidimension
 

Hi ag, Thanks for your response. I figured out some thing... In the HLL flux calculation, when I compute the fluxes (left and right), I calculated them in X and Y directions. But, I used the wave amplitudes to be in the normal direction. This was unstable. However, when I used the FL and FR to be along the normal direction, the problem was solved. I dont know if it was a bug in my code, which I rectified without my knowledge, or the treatment of fluxes made a difference. Anyway, for now, I guess it works fine.

Re: Riemann Solvers in multidimension
 

I am surprised about HLLC not working for non Cartesian meshes. For a rotational invariant system, you first rotate the data in the direction normal to the face, calculate the HLLC, or any other, and then rotate back. See chapt 16 of Toro E F. Riemann solbvers and numerical methods for fluid dynamics. Springer 1999.

EF Toro

Re: Riemann Solvers in multidimension
 

Hi,

Thanks for your input. I corrected my code, and it works!!

The book also gives multiple options for wave speed estimates, and I find that for a solution containing shock, these wave speed estimates play a significant role. Can you suggest me a good wave speed estimate?

Regards, DSS