High-Order FVM
 

Hi, All! Could you please tell me whether there are some high-order meshes (like the one used used in FEM) available for FVM? Thank you and have a good weekend!

David

Re: High-Order FVM
 

If you use an FVEM (or discontinuous Galerkin) scheme, you will be able to use higher-order interpolation functions. For these methods, you can choose the appropriate interpolation functions for the type of problems you are dealing with. Since, the weight functions are constant by cells (one over the cell, zero elsewhere), you end up with a Finite Volume scheme. Nevertheless, it will be harder to construct a stable scheme.

Re: High-Order FVM
 

Maybe by choosing better method to compute the gradient of the cell center , you can get more accurate values on the interface of a control volume, then you can compute more accurate numeric flux.

You may use Green theorem, or least square method to calculate gradient. Someone use Green theorem to get third order result.