Gradient Estimation for Higher Order Schemes

jianxia

Hi,friends, For high order finite volume method, it is necessary to using Gauss Theorem to construct the solution gradient. For vertex-centered scheme, it is easy. But for cell centered scheme, if we choose the cell self as the control volume and choose the perimeter of the cell(the values on the boundary are estimated by the arithmetic average of the cell values and the neigbour cell values, I think it is not accurate enough. Is there any methods(for arbitray meshs)? Thanks.