A class of Reconstructed Discontinuous Galerkin Methods for Compressible Flows on Arbitrary Grids

Hong Luo, Yidong Xia, Robert Norgaliev, Chunpei Cai
2011 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition   unpublished
A class of reconstructed discontinuous Galerkin methods is described for solving compressible flow problems on arbitrary grids. Both Green-Gauss and least-squares reconstruction methods and a least-squares recovery method are presented to obtain a quadratic polynomial representation of the underlying linear discontinuous Galerkin solution on each cell via a so-called in-cell reconstruction process. The devised in-cell reconstruction is aimed to augment the accuracy of the discontinuous Galerkin
more » ... continuous Galerkin method by increasing the order of the underlying polynomial solution. These three reconstructed discontinuous Galerkin methods are used to compute a variety of compressible flow problems on arbitrary meshes to assess their accuracy. The numerical experiments demonstrate that all three reconstructed discontinuous Galerkin methods can significantly improve the accuracy of the underlying second-order DG method, although the least-squares reconstruction method provides the best performance in terms of both accuracy, efficiency, and robustness 1 Associate Professor, Department of Mechanical and Aerospace Engineering, Senior Member AIAA.
doi:10.2514/6.2011-199 fatcat:7thelsa3ybdnngr74t6a3rqf3q