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

Part of: Hyperbolic equations and systems Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  27 March 2017

Jian Cheng ,
Xiaodong Liu ,
Tiegang Liu  and
Hong Luo
Jian Cheng*
Affiliation:
School of Mathematics and Systems Science, Beihang University, Beijing 100191, P.R. China
Xiaodong Liu*
Affiliation:
Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC, 27695, USA
Tiegang Liu*
Affiliation:
School of Mathematics and Systems Science, Beihang University, Beijing 100191, P.R. China
Hong Luo*
Affiliation:
Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC, 27695, USA
*
*Corresponding author. Email addresses:chengjian@buaa.edu.cn (J. Cheng), xliu29@ncsu.edu (X. Liu), liutg@buaa.edu.cn (T. Liu), hong_luo@ncsu.edu (H. Luo)
*Corresponding author. Email addresses:chengjian@buaa.edu.cn (J. Cheng), xliu29@ncsu.edu (X. Liu), liutg@buaa.edu.cn (T. Liu), hong_luo@ncsu.edu (H. Luo)
*Corresponding author. Email addresses:chengjian@buaa.edu.cn (J. Cheng), xliu29@ncsu.edu (X. Liu), liutg@buaa.edu.cn (T. Liu), hong_luo@ncsu.edu (H. Luo)
*Corresponding author. Email addresses:chengjian@buaa.edu.cn (J. Cheng), xliu29@ncsu.edu (X. Liu), liutg@buaa.edu.cn (T. Liu), hong_luo@ncsu.edu (H. Luo)
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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 methodcompressible Navier-Stokes equationshybrid grids

MSC classification

Secondary: 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65M99: None of the above, but in this section 35L65: Conservation laws
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 5 , May 2017 , pp. 1231 - 1257
Copyright
Copyright © Global-Science Press 2017 

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