Viscous flow simulation using an upwind method for hexahedral based adaptive meshes

Abstract

Abstract : Details of an adaptive, high resolution, upwind algorithm for the simulation of viscous flows on unstructured hexahedral meshes are presented. The method used a TVD scheme for modeling the inviscid terms while the viscous terms rely upon central differencing. Grid adaptation is achieved through directional division of hexahedral cells in response to flow features. The discussion focuses primarily on details of the new viscous discretization and evaluates it through example problems, analysis and mathematical proof. Several issues facing the development of upwind schemes on adaptive, unstructured meshes are prominently discussed. The test cases examine issues of consistency and mesh convergence of the adaptive methodology and the ability of the adaptation to accurately resolve flows which require detailed resolution of subtle flow features. These examples point out several general issues regarding the interaction of the upwind inviscid discretization with the centrally differenced viscous terms, especially near inviscid stagnation points, and within the boundary layer itself. A technique for avoiding the appearance of anomalous solutions in such regions is presented and discussed.