Comparison and Unification of Finite-Volume Discretization Strategies for the Unstructured Node-Centered and Cell-Centered Grid Metric in TAU and CODA

Abstract

2nd order finite-volume discretization schemes generally offer a good compromise between computational effort and accuracy. For a given mesh, the accuracy of an approximate solution often depends significantly on the discretization applied to the underlying grid. Therefore, the discretization has to be adapted to the chosen grid metric, including the types of elements present in the mesh. To keep the number of degrees of freedom acceptable, in regions of the grid, where steep gradients need to be resolved, quadrilateral, hexahedral or prismatic elements with an extreme cell-stretching are required. Hence, one is now forced to develop unstructured discretizations that reliably produce accurate solutions for mixed grids with elements of high anisotropies. In this work we review and demonstrate, in which way these anisotropies can be meaningfully incorporated into different, commonly used discretization schemes and how the schemes can be extended for unstructured grids in order to achieve good quality solutions.