A Discontinuous Galerkin Chimera scheme

Abstract

The Chimera overset method is a powerful technique for modeling fluid flow associated with complex engineering problems using structured meshes. The use of structured meshes has enabled engineers to employ a number of high-order schemes, such as the WENO and compact differencing schemes. However, the large stencil associated with these schemes can significantly complicate the inter-grid communication scheme and hole cutting procedures. This paper demonstrates a methodology for using the Discontinuous Galerkin (DG) scheme with Chimera overset meshes. The small stencil of the DG scheme makes it particularly suitable for Chimera meshes as it simplifies the inter-grid communication scheme as well as hole cutting procedures. The DG-Chimera scheme does not require a donor interpolation method with a large stencil because the DG scheme represents the solution as cell local polynomials. The DG-Chimera method also does not require the use of fringe points to maintain the interior stencil across inter-grid boundaries. Thus, inter-grid communication can be established as long as the receiving boundary is enclosed by or abuts the donor mesh. This makes the inter-grid communication procedure applicable to both Chimera and zonal meshes. Details of the DG-Chimera scheme are presented, and the method is demonstrated on a set of two-dimensional inviscid flow problems.