Flux balanced approximation with least-squares gradient for diffusion equation on polyhedral mesh
The authors present a finite volume method for the diffusion equations that can be applied to general polyhedral meshes. It is based on the flux balanced approximation using the least-squares gradient with the distance weighted harmonic mean of piecewise continuous diffusion coefficient. The degrees of freedom are the values at the centers of the cells. The flux balanced approximation is proposed without numerically computing the gradient itself at the faces of computational cells in order to find a normal diffusive flux. It is shown that in the case of discontinuous diffusion coefficient, it is suitable to use the restricted least-squares gradient that respects the discontinuity in the approximation. The method can be used in the iterative way, where each iteration uses a matrix in the 1-ring neighborhood. Several numerical examples are presented to illustrate some advantages of the proposed method.
scientific article; zbMATH DE number 7345415