Differential Formulation of Discontinuous Galerkin and Related Methods for the Navier-Stokes Equations

作     者：Haiyang Gao Z.J.Wang H.T.Huynh 

作者机构：Department of Aerospace Engineering and CFD CenterIowa State University2271 Howe Hall AmesIA 50011USA NASA Glenn Research CenterMS 5-11ClevelandOH 44135USA 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2013年第13卷第4期

页      面：1013-1044页

核心收录：

学科分类：07[理学] 0704[理学-天文学] 0701[理学-数学] 0702[理学-物理学] 070101[理学-基础数学] 

基　　金：funded by AFOSR grant FA9550-06-1-0146 

主　　题：Discontinuous Galerkin lifting collocation penalty flux reconstruction Navier-Stokes equations correction procedure via reconstruction unstructured hybrid grids 

摘      要：A new approach to high-order accuracy for the numerical solution of conservation laws introduced by Huynh and extended to simplexes by Wang and Gao is renamed CPR(correction procedure or collocation penalty via reconstruction).The CPR approach employs the differential form of the equation and accounts for the jumps in flux values at the cell boundaries by a correction *** addition to being simple and economical,it unifies several existing methods including discontinuous Galerkin,staggered grid,spectral volume,and spectral *** discretize the diffusion terms,we use the BR2(Bassi and Rebay),interior penalty,compact DG(CDG),and I-continuous *** first three of these approaches,originally derived using the integral formulation,were recast here in the CPR framework,whereas the I-continuous scheme,originally derived for a quadrilateral mesh,was extended to a triangular *** stability and accuracy analyses for these schemes on quadrilateral and triangular meshes are carried ***,results for the Navier-Stokes equations are shown to compare the various schemes as well as to demonstrate the capability of the CPR approach.