Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Inviscid Fluxes

摘要: Discretization of the viscous terms in current finite-volume unstructured-grid schemes are compared using node-centered and cell-centered approaches two dimensions. Accuracy efficiency studied for six nominally second-order accurate schemes: a scheme, node-averaging with without clipping, unweighted, weighted, approximately mapped least-square face gradient reconstruction. The grids considered range from structured (regular) to irregular composed arbitrary mixtures triangles quadrilaterals, including random perturbations grid points bring out worst possible behavior solution. Two classes tests considered. first class involves smooth manufactured solutions on both isotropic highly anisotropic discontinuous metrics, typical those encountered adaptation. second concerns varying strongly anisotropically over curved body, high-Reynolds number turbulent flow simulations. Results indicate methods, method demonstrate convergence discretization errors very similar accuracies per degree freedom. more discriminating. scheme is always order an accuracy complexity linearization comparable best schemes. In comparison, nodeaveraging less accurate, have higher linearization, can fail converge exact solution when clipping node-averaged values used. reconstruction compact stencils that scheme. For simulations grids, methods be amended either by introducing local mapping surface based distance function commonly available practical or modifying stencil reflect direction strong coupling. major conclusion node centered at equivalent degrees