A Parallel, High-Order Direct Discontinuous Galerkin Method for the Navier-Stokes Equations on 3D Hybrid Grids. (27th March 2017)

• Record Type: Journal Article
• Authors: Cheng, Jian; Liu, Xiaodong; Liu, Tiegang; Luo, Hong
• Is Part Of: Communications in computational physics. Volume 21:Number 5(2017:May)
• Page Start: 1231
• Page End: 1257
• Publication Date: 2017-03-27
• Subjects: 65M60, -- 65M99, -- 35L65; Direct discontinuous Galerkin method, -- compressible Navier-Stokes equations, -- hybrid grids; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.OA-2016-0090
• Languages: English
• ISSNs: 1815-2406

Abstract

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.