am a Ph.D student from Singapore and trying to implement the Dynamic Mixed Model for our compressible LES code. Our solver is vertex-based finite volume scheme on unstructured grids. A cell-vertex scheme is adopted here, i.e., all computed variables in dependent vector are stored at vertices of the triangular cell. For every vertex, a control volume is constructed by joining the centers of the cell to the centre of the edges using the median dual of the triangular grid. This configuration implies that the number of neighboring control volumes is a random value.

My problems lay in following areas:

1). What I am trying to use is a linear combination of the scale-similarity model and Germano-Lilly model. To compute the test-filtered variables, as well as the double basic filtered ones, we just use simple volume averaging. But the results seem not very good. I can't find any more information on the explicit filter implementation details on unstructured grids. Could you give me some details on it?

2). Our LES code seems not very stable on the boundary, especially on the far field inflow and outflow. In the current implementation, we don't introduce any special treatments after the integration of LES models. Are there any cautions we need to take care of for the boundary treatments in LES?

3). In the filtered energy equation, I have 5 terms to be modeled. Among them, some terms just can not be transferred to divergence form, which could be a problem in the traditional Finite Volume scheme. Could you give me some suggestions on how to deal with these terms for FV schemes?

Thank you very much for your time! Any suggestions are much appreciated!

I know there should someone who can help me!

The implementation is based on the discrete interpolation filters proposed by Marsden. Testing results show that the it is very stable and accurate.