TY - JOUR
T1 - A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids
AU - Hong Luo, Luqing Luo & Robert Nourgaliev
JO - Communications in Computational Physics
VL - 5
SP - 1495
EP - 1519
PY - 2012
DA - 2012/12
SN - 12
DO - http://doi.org/10.4208/cicp.250911.030212a
UR - https://global-sci.org/intro/article_detail/cicp/7344.html
KW - 
AB - <p style="text-align: justify;">A reconstruction-based discontinuous Galerkin (RDG(P1P2)) method, avariant 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.&nbsp;</p>