Mesh Adaptation for Curing the Pathological Behaviors of an Upwind Scheme

Abstract

In present paper, mesh adaptation is applied for curing the pathological behaviors of the enhanced time-accurate upwind scheme (Loh & Jorgenson, AIAAJ 2016). In the original ETAU (enhanced time-accurate upwind) scheme, a multi-dimensional dissipation model is required to cure the pathological behaviors. The multi-dimensional dissipation model will increase the global dissipation level reducing numerical resolution. In present work, the metric-based mesh adaptation strategy provides an alternative way to cure the pathological behaviors of the shock capturing. The Hessian matrix of flow variables is applied to construct the metric, which represents the curvature of the physical solution. The adapting operation can well refine the anisotropic meshes at the location with large gradients. The numerical results show that the adaptation of mesh provides a possible way to cure the pathological behaviors of upwind schemes.