A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids

作者：Luo Hong^*; Luo Luqing; Nourgaliev Robert

来源：Communications in Computational Physics, 2012, 12(5): 1495-1519.

DOI：10.4208/cicp.250911.030212a

• Discontinuous Galerkin methods
• least-squares reconstruction
• compressible Euler equations

A reconstruction-based discontinuous Galerkin (RDG(P1P2)) method, a variant of P1P2 method, is presented for the solution of the compressible Euler equations on arbitrary grids. In this method, an in-cell reconstruction, designed to enhance the accuracy of the discontinuous Galerkin method, is used to obtain a quadratic polynomial solution (P2) from the underlying linear polynomial (P1) discontinuous Galerkin solution using a least-squares method. The stencils used in the reconstruction involve only the von Neumann neighborhood (face-neighboring cells) and are compact and consistent with the underlying DG method. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG(P1P2) method is third-order accurate, and outperforms the third-order DG method (DG(P2)) in terms of both computing costs and storage requirements.

• 出版日期2012-11