A Novel Eighth-Order Diffusive Scheme for Unstructured Polyhedral Grids Using the Weighted Least-Squares Method

Abstract

AbstractA new very high-order scheme for elliptic operators in unstructured polyhedral grids is proposed, based on the weighted least-squares technique. It can go up to eighth-order accuracy and uses face centred reconstructions for the integration of the diffusive fluxes. In order to maintain the local high-order, a new stencil extension algorithm is applied near the boundaries of the computational domain. The algorithm maintains the intended accuracy order independently of the grid type or the perturbation imposed to the grid. Concerning Neumann boundary conditions, a new approach is proposed that is better than the classic one used in schemes based in weighted least-squares.