A Discontinuous Galerkin Chimera scheme

Abstract

a b s t r a c tThe 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.Published by Elsevier Ltd.

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

“…Numerical experiments by Galbraith et. al [22] indicate that increasing Gauss-Quadrature node count beyond N GQ ¼ 3N=2 d eþ1 does not significantly reduce the error.…”

“…6c. Galbraith et al [22] obtained Euler solutions using a zonal interface with mixed geometric representations of the two meshes.…”

“…(1) are approximated with the average solution on the face, and upwind dissipation, /, is added through the Roe approximate Riemann solver [26]. The boundary and volume integrals associated with the viscous flux are modified by adding the lifting operator,r, in accords with the BR2 discretization scheme [15,22]. Hence, the final discrete weak form of Eq.…”

“…In this paper, the DG-Chimera scheme presented in Ref. [22] is extended to include viscous terms, and the primary focus is computing laminar flows with viscous Chimera meshes with non-co-located artificial boundaries on curved geometries. In this situation, meshes based on linear cells, which are used for finite volume (FV) and finite difference (FD) schemes, will not produce the valid interpolation; unless they are corrected using, for example, the ''Projection'' features in PEGASUS5 [19,20] and SUGGAR++ [21].…”

An overset mesh approach for 3D mixed element high-order discretizations

“…Recently, DG has been used in an overset framework to solve the two-dimensional, Euler equations on abutting and overset grids [30]. Flux Reconstruction (FR) has been used to solve the two-dimensional, compressible Navier-Stokes equations on sliding meshes [31].…”