Volume 21, Issue 5
A Parallel, High-Order Direct Discontinuous Galerkin Method for the Navier-Stokes Equations on 3D Hybrid Grids

Jian Cheng, Xiaodong Liu, Tiegang Liu & Hong Luo

Commun. Comput. Phys., 21 (2017), pp. 1231-1257.

Published online: 2019-10

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  • Abstract

A parallel, high-order direct Discontinuous Galerkin (DDG) method has been developed for solving the three dimensional compressible Navier-Stokes equations on 3D hybrid grids. The most distinguishing and attractive feature of DDG method lies in its simplicity in formulation and efficiency in computational cost. The formulation of the DDG discretization for 3D Navier-Stokes equations is detailed studied and the definition of characteristic length is also carefully examined and evaluated based on 3D hybrid grids. Accuracy studies are performed to numerically verify the order of accuracy using flow problems with analytical solutions. The capability in handling curved boundary geometry is also demonstrated. Furthermore, an SPMD (single program, multiple data) programming paradigm based on MPI is proposed to achieve parallelism. The numerical results obtained indicate that the DDG method can achieve the designed order of accuracy and is able to deliver comparable results as the widely used BR2 scheme, clearly demonstrating that the DDG method provides an attractive alternative for solving the 3D compressible Navier-Stokes equations.

  • Keywords

Direct discontinuous Galerkin method, compressible Navier-Stokes equations, hybrid grids.

  • AMS Subject Headings

65M60, 65M99, 35L65

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

chengjian@buaa.edu.cn (Jian Cheng)

xliu29@ncsu.edu (Xiaodong Liu)

liutg@buaa.edu.cn (Tiegang Liu)

hong luo@ncsu.edu (Hong Luo)

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@Article{CiCP-21-1231, author = {Cheng , Jian and Liu , Xiaodong and Liu , Tiegang and Luo , Hong }, title = {A Parallel, High-Order Direct Discontinuous Galerkin Method for the Navier-Stokes Equations on 3D Hybrid Grids}, journal = {Communications in Computational Physics}, year = {2019}, volume = {21}, number = {5}, pages = {1231--1257}, abstract = {

A parallel, high-order direct Discontinuous Galerkin (DDG) method has been developed for solving the three dimensional compressible Navier-Stokes equations on 3D hybrid grids. The most distinguishing and attractive feature of DDG method lies in its simplicity in formulation and efficiency in computational cost. The formulation of the DDG discretization for 3D Navier-Stokes equations is detailed studied and the definition of characteristic length is also carefully examined and evaluated based on 3D hybrid grids. Accuracy studies are performed to numerically verify the order of accuracy using flow problems with analytical solutions. The capability in handling curved boundary geometry is also demonstrated. Furthermore, an SPMD (single program, multiple data) programming paradigm based on MPI is proposed to achieve parallelism. The numerical results obtained indicate that the DDG method can achieve the designed order of accuracy and is able to deliver comparable results as the widely used BR2 scheme, clearly demonstrating that the DDG method provides an attractive alternative for solving the 3D compressible Navier-Stokes equations.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2016-0090}, url = {http://global-sci.org/intro/article_detail/cicp/13344.html} }
TY - JOUR T1 - A Parallel, High-Order Direct Discontinuous Galerkin Method for the Navier-Stokes Equations on 3D Hybrid Grids AU - Cheng , Jian AU - Liu , Xiaodong AU - Liu , Tiegang AU - Luo , Hong JO - Communications in Computational Physics VL - 5 SP - 1231 EP - 1257 PY - 2019 DA - 2019/10 SN - 21 DO - http://dor.org/10.4208/cicp.OA-2016-0090 UR - https://global-sci.org/intro/cicp/13344.html KW - Direct discontinuous Galerkin method, compressible Navier-Stokes equations, hybrid grids. AB -

A parallel, high-order direct Discontinuous Galerkin (DDG) method has been developed for solving the three dimensional compressible Navier-Stokes equations on 3D hybrid grids. The most distinguishing and attractive feature of DDG method lies in its simplicity in formulation and efficiency in computational cost. The formulation of the DDG discretization for 3D Navier-Stokes equations is detailed studied and the definition of characteristic length is also carefully examined and evaluated based on 3D hybrid grids. Accuracy studies are performed to numerically verify the order of accuracy using flow problems with analytical solutions. The capability in handling curved boundary geometry is also demonstrated. Furthermore, an SPMD (single program, multiple data) programming paradigm based on MPI is proposed to achieve parallelism. The numerical results obtained indicate that the DDG method can achieve the designed order of accuracy and is able to deliver comparable results as the widely used BR2 scheme, clearly demonstrating that the DDG method provides an attractive alternative for solving the 3D compressible Navier-Stokes equations.

Jian Cheng, Xiaodong Liu, Tiegang Liu & Hong Luo. (2019). A Parallel, High-Order Direct Discontinuous Galerkin Method for the Navier-Stokes Equations on 3D Hybrid Grids. Communications in Computational Physics. 21 (5). 1231-1257. doi:10.4208/cicp.OA-2016-0090
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