Edge-based anisotropic mesh adaptation of unstructured meshes with applications to compressible flows

Abstract

An adaptation procedure using refinement, coarsening and smoothing with anisotropic considerations for unstructured meshes and its coupling with a compressible flow solver is presented in this work. The developed refinement strategy combines a Riemannian centred split of the edges. The coarsening methodology uses an edge collapse procedure where the collapse point is evaluated using anisotropic quality considerations. An accurate and anisotropic vertex smoothing algorithm that operates along the direction of the edges is presented. Edge and face swapping are also used together with the refinement coarsening and smoothing strategies to enhance anisotropic quality. The developed approach makes use of only simple mesh information and is applicable to two and three-dimensional meshes. The performance of the methodology is analysed for two-dimensional triangular meshes and three-dimensional tetrahedral meshes on analytical test cases and to solve steady-state inviscid compressible flows. The transonic flow past an airfoil, the supersonic flow around a sphere and the flow around a complex real-life application are performed.