Mesh curving techniques for high order discontinuous Galerkin simulations

Abstract

In the development of the next generation of numerical methods for CFD, Discontinuous Galerkin methods are promising a substantial increase in efficiency and accuracy. While the particular high order methods can be very distinct, they have in common that they must rely on a high-order approximation of curved geometries to maintain their high-order of accuracy. The generation of curved meshes is thus a topic whose importance cannot be overstated, if one truly wants to apply DG methods to problems with industrial relevance. Especially aerospace applications heavily rely on complex geometries and pose high requirements to the quality of geometry representation. In this work we present several techniques to produce high order meshes, relying on linear meshes, which can be generated by standard commercial mesh generation tools. We describe the generation of the curved surface meshes and curved volume meshes, which can be particularly difficult for curved boundary layers.