A 3-D Discontinuous Galerkin Chimera Overset Method

The Chimera overset method is a powerful technique for numerically solve partial differential equations associated with complex engineering problems using arbitrarily overlapping meshes. The method has allowed engineers to apply high-order schemes, such as the WENO and compact di erencing, which require structured meshes, to complex geometric con gurations. However, the large stencil associated with these high-order schemes can signi cantly complicate hole cutting procedures and the inter-grid communication scheme; particularly for three-dimensional geometries. This paper demonstrates a methodology for using the Discontinuous Galerkin (DG) scheme with Chimera overset meshes in threedimensions. The small stencil of the DG scheme makes it particularly suitable for Chimera meshes as it simpli es the inter-grid communication scheme. In addition, because the DG scheme represents the solution as cell local polynomials, the DG-Chimera scheme does not require a donor interpolation method with a large stencil. 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 so long as the receiving boundary is enclosed by or abuts with the donor mesh. This makes the inter-grid communication procedure applicable to both Chimera and zonal meshes. Details of threedimensional DG-Chimera scheme are presented, and the method is demonstrated on a set of inviscid ow problems.

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