Anisotropic mesh generation and adaptation for quads using the Lp-CVT method

Abstract

This paper presents a framework for anisotropic unstructured all-quad mesh adaptation. The technique is suitable for use with a diverse class of numerical methods, including the high-order Discontinuous Galerkin solver presented here. Benefiting from the flexibility and efficiency of these methods, improvements in the solution accuracy are targeted by modifying the discretization of the domain. Previous works have tackled this problem for the case of simplex elements using continuous mesh and error models. Our method makes use of novel extensions to allow similar techniques to be applied for the case of tensor product elements. Key aspects of the work will discuss the modified continuous mesh representation and error minimization procedure. Additionally, these ideas have been coupled with mesh generation based on both existing and experimental techniques. As a result, this work will also consider the implementation of an energy minimizing, node redistribution method, that takes place in an anisotropic spatially varying high-order p-norm. Finally, the technique will also be applied to goal-oriented adaption using the adjoint-based error estimation. Overall, the work outlines the adaptive procedure tailored specially to all-quad meshing.