@Article{CiCP-9-363,
author = {Hong Luo, Luqing Luo, Amjad Ali, Robert Nourgaliev and Chunpei Cai},
title = {A Parallel, Reconstructed Discontinuous Galerkin Method for the Compressible Flows on Arbitrary Grids},
journal = {Communications in Computational Physics},
year = {2011},
volume = {9},
number = {2},
pages = {363--389},
abstract = {<p style="text-align: justify;">A reconstruction-based discontinuous Galerkin method is presented for the
solution of the compressible Navier-Stokes equations on arbitrary grids. In this method,
an in-cell reconstruction is used to obtain a higher-order polynomial representation
of the underlying discontinuous Galerkin polynomial solution and an inter-cell reconstruction
is used to obtain a continuous polynomial solution on the union of two
neighboring, interface-sharing cells. The in-cell reconstruction is designed to enhance
the accuracy of the discontinuous Galerkin method by increasing the order of the underlying
polynomial solution. The inter-cell reconstruction is devised to remove an
interface discontinuity of the solution and its derivatives and thus to provide a simple,
accurate, consistent, and robust approximation to the viscous and heat fluxes
in the Navier-Stokes equations. A parallel strategy is also devised for the resulting
reconstruction discontinuous Galerkin method, which is based on domain partitioning
and Single Program Multiple Data (SPMD) parallel programming model. The
RDG method is used to compute a variety of compressible flow problems on arbitrary
meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The
numerical results demonstrate that this RDG method is third-order accurate at a cost
slightly higher than its underlying second-order DG method, at the same time providing
a better performance than the third order DG method, in terms of both computing
costs and storage requirements.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.070210.020610a},
url = {http://global-sci.org/intro/article_detail/cicp/7503.html}
}