Mesh Adaptation for Curing the Pathological Behaviors of an Upwind Scheme (Communications in Computational Physics, 2022)
In present paper, mesh adaptation is applied for curing the pathologicalbehaviors of the enhanced time-accurate upwind scheme (Loh & Jorgenson, AIAAJ2016). In the original ETAU (enhanced time-accurate upwind) scheme, a multi-dimensional dissipation model is required to cure the pathological behaviors. Themulti-dimensional dissipation model will increase the global dissipation level reducing numerical resolution. In present work, the metric-based mesh adaptation strategyprovides an alternative way to cure the pathological behaviors of the shock capturing. The Hessian matrix of flow variables is applied to construct the metric, whichrepresents the curvature of the physical solution. The adapting operation can well refine the anisotropic meshes at the location with large gradients. The numerical resultsshow that the adaptation of mesh provides a possible way to cure the pathologicalbehaviors of upwind schemes.