scholarly journals A third-order implicit discontinuous Galerkin method based on a Hermite WENO reconstruction for time-accurate solution of the compressible Navier-Stokes equations

2015 ◽  
Vol 79 (8) ◽  
pp. 416-435 ◽  
Author(s):  
Yidong Xia ◽  
Xiaodong Liu ◽  
Hong Luo ◽  
Robert Nourgaliev
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Stokes Equations ◽  
Accurate Solution ◽  
Navier Stokes ◽  
Weno Reconstruction ◽  
Third Order ◽  
Navier Stokes Equations

A Parallel, Reconstructed Discontinuous Galerkin Method for the Compressible Flows on Arbitrary Grids

2011 ◽  
Vol 9 (2) ◽  
pp. 363-389 ◽  
Author(s):  
Hong Luo ◽  
Luqing Luo ◽  
Amjad Ali ◽  
Robert Nourgaliev ◽  
Chunpei Cai
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Compressible Flows ◽  
Stokes Equations ◽  
Polynomial Solution ◽  
Navier Stokes ◽  
Third Order ◽  
Navier Stokes Equations ◽  
Dg Method

AbstractA 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.

scholarly journals Numerical solution of the Navier-Stokes equations by discontinuous Galerkin method

2017 ◽  
Vol 815 ◽  
pp. 012015 ◽  
Author(s):  
M M Krasnov ◽  
P A Kuchugov ◽  
M E Ladonkina ◽  
A E Lutsky ◽  
V F Tishkin
Keyword(s):  
Galerkin Method ◽  
Numerical Solution ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations
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