A very high-order finite volume method based on weighted least squares for elliptic operators on polyhedral unstructured grids

摘要: Abstract A very high-order finite volume method is proposed for the solution of Poisson equation on unstructured grids based weighted least-squares method. The new consists in an up to eight-order accurate face centered reconstruction integration diffusive fluxes. It uses a stencil extension algorithm that maintains local near boundaries computational domain. weight function used by scheme was optimized according matrix condition number, convergence order and error magnitude. From this study type schemes which achieves theoretical Cartesian, triangular, polyhedral hybrid grids. An Neumann boundary conditions also shown. grid quality study, non-orthogonality angle ratio, proves scheme’s not affected these parameters. efficiency criteria, defined required memory solver-run time, indicate advantageous over lower ones, additionally it demonstrated yields more efficient solutions than ones obtained with Cartesian or triangular