A discontinuous Galerkin scheme for Chimera overset viscous meshes on curved geometries

Abstract

The Chimera overset method is a powerful technique for modeling fluid flow associated with complex engineering problems. The use of structured meshes has enabled engineers to develop a number of high-order schemes, such as the WENO and compact differencing schemes. This paper demonstrates a Discontinuous Galerkin (DG) scheme with a Chimera overset method applied to viscous meshes on curved geometries. The small stencil of the DG scheme makes it particularly suitable for Chimera meshes. The small stencil simplifies the hole cutting and partitioning of grids that contain holes. In addition, because the DG scheme represents the solution as cell local polynomials, it does not require an interpolation scheme with a large stencil to establish the inter-grid communication in overlapping regions. Furthermore, the DG scheme is capable of using curved cells to represent geometric features. The curved cells resolve issues associated with linear non-co-located Chimera viscous meshes used for finite volume and finite difference schemes. The DG-Chimera method is demonstrated on a set of viscous Chimera meshes, which would produce erroneous results for a finite volume or finite difference scheme without corrections to the interpolation.