A Parallel, Reconstructed Discontinuous Galerkin Method for the Compressible Flows on Arbitrary Grids (Communications in Computational Physics, 2018)
A reconstruction-based discontinuous Galerkin method is presented for thesolution of the compressible Navier-Stokes equations on arbitrary grids. In this method,an in-cell reconstruction is used to obtain a higher-order polynomial representationof the underlying discontinuous Galerkin polynomial solution and an inter-cell reconstructionis used to obtain a continuous polynomial solution on the union of twoneighboring, interface-sharing cells. The in-cell reconstruction is designed to enhancethe accuracy of the discontinuous Galerkin method by increasing the order of the underlyingpolynomial solution. The inter-cell reconstruction is devised to remove aninterface discontinuity of the solution and its derivatives and thus to provide a simple,accurate, consistent, and robust approximation to the viscous and heat fluxesin the Navier-Stokes equations. A parallel strategy is also devised for the resultingreconstruction discontinuous Galerkin method, which is based on domain partitioningand Single Program Multiple Data (SPMD) parallel programming model. TheRDG method is used to compute a variety of compressible flow problems on arbitrarymeshes to demonstrate its accuracy, efficiency, robustness, and versatility. Thenumerical results demonstrate that this RDG method is third-order accurate at a costslightly higher than its underlying second-order DG method, at the same time providinga better performance than the third order DG method, in terms of both computingcosts and storage requirements.