Transient adaptation
 

Dear Friends,

I am working on transient adaptation and presently faced with a problem. I have considered a standard 2-D Riemann problem ( 4 states in the 4 quadrants ) and try to solve it starting from an initial coarse grid. For the present problem where the simulation time is 0.3s, I have perfomed an adaptation in every 10 steps. I have used 100 steps in total with a physical time step of 0.003s. The problem is solved using a cell-centered finite volume scheme on a cartesian grid with limiting and linear reconstruction using Roe scheme and Dual time stepping.

The trouble is the final solution is not quite in match with the results on a fine mesh, which means there is some trouble in solution advancement. I understand that it is critical that the conservation be preserved when we advance in time. Thus when we transfer the solution from a coarse mesh to a finer mesh, this has to be taken care of. I have tried the following options

1. The values in the coarser cell is directly supplied as such to its children. 2. The values in the coarser cell are supplied to children by using a linear interpolation. ( Ham,Lien and Strong, JCP 2002)

However, in both cases I still do not manage to get the right solution. I am not clear if my solution transfer procedure is right, but I understand the first one is not quite right.

Could you please give your suggestions or references to this problem

Thanks in advance,

Ganesh