A DPG method for steady viscous compressible flow

被引：29
作者：
Chan, Jesse [1 ]
Demkowicz, Leszek [2 ]
Moser, Robert [2 ]
机构：
[1] Rice Univ, Houston, TX 77005 USA
[2] Univ Texas Austin, Inst Computat Engn & Sci, Austin, TX 78712 USA
来源：
COMPUTERS & FLUIDS | 2014年 / 98卷
关键词：
Petrov-Galerkin; Minimum residual; Higher order; Adaptivity; Anisotropic mesh refinement; Convection-diffusion; Burgers equation; Compressible Navier-Stokes; NAVIER-STOKES EQUATIONS; FINITE-ELEMENT-METHOD; COMPUTATIONAL FLUID-DYNAMICS; DOMINATED DIFFUSION-PROBLEMS; P-VERSION; GALERKIN; FORMULATION; ADAPTIVITY; EULER;
D O I：
10.1016/j.compfluid.2014.02.024
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
The Discontinuous Petrov-Galerkin (DPG) method is a class of novel higher order adaptive finite element methods derived from the minimization of the residual of the variational problem (Demkowicz and Gopalakrishnan, 2011) [1], and has been shown to deliver a method for convection diffusion that is provably robust in the diffusion parameter (Demkowicz and Heuer, in press; Chan et al., in press) [2,3]. In this work, the DPG method is extrapolated to nonlinear systems, and applied to several problems in fluid dynamics whose solutions exhibit boundary layers or singularities in stresses. In particular, the effectiveness of DPG as a numerical method for compressible flow is assessed with the application of DPG to two model problems over a range of Mach numbers and laminar Reynolds numbers using automatic adaptivity with higher order finite elements, beginning with highly under-resolved coarse initial meshes. (C) 2014 Elsevier Ltd. All rights reserved.
引用
收藏
页码：69 / 90
页数：22
相关论文
共 41 条
[11]  
Chan J. L., 2013, 1305 ICES
[12]   A robust DPG method for convection-dominated diffusion problems II: Adjoint boundary conditions and mesh-dependent test norms [J].
Chan, Jesse ;
Heuer, Norbert ;
Tan Bui-Thanh ;
Demkowicz, Leszek .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2014, 67 (04) :771-795
[13]   UNIFIED HYBRIDIZATION OF DISCONTINUOUS GALERKIN, MIXED, AND CONTINUOUS GALERKIN METHODS FOR SECOND ORDER ELLIPTIC PROBLEMS [J].
Cockburn, Bernardo ;
Gopalakrishnan, Jayadeep ;
Lazarov, Raytcho .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2009, 47 (02) :1319-1365
[14]   A NEW FINITE-ELEMENT METHOD FOR SOLVING COMPRESSIBLE NAVIER-STOKES EQUATIONS BASED ON AN OPERATOR SPLITTING METHOD AND H-P ADAPTIVITY [J].
DEMKOWICZ, L ;
ODEN, JT ;
RACHOWICZ, W .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1990, 84 (03) :275-326
[15]   A primal DPG method without a first-order reformulation [J].
Demkowicz, L. ;
Gopalakrishnan, J. .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2013, 66 (06) :1058-1064
[16]   ANALYSIS OF THE DPG METHOD FOR THE POISSON EQUATION [J].
Demkowicz, L. ;
Gopalakrishnan, J. .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2011, 49 (05) :1788-1809
[17]   A Class of Discontinuous Petrov-Galerkin Methods. II. Optimal Test Functions [J].
Demkowicz, L. ;
Gopalakrishnan, J. .
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2011, 27 (01) :70-105
[18]   A class of discontinuous Petrov-Galerkin methods. Part I: The transport equation [J].
Demkowicz, L. ;
Gopalakrishnan, J. .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2010, 199 (23-24) :1558-1572
[19]   ROBUST DPG METHOD FOR CONVECTION-DOMINATED DIFFUSION PROBLEMS [J].
Demkowicz, Leszek ;
Heuer, Norbert .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2013, 51 (05) :2514-2537
[20]   A class of discontinuous Petrov-Galerkin methods. Part III: Adaptivity [J].
Demkowicz, Leszek ;
Gopalakrishnan, Jay ;
Niemi, Antti H. .
APPLIED NUMERICAL MATHEMATICS, 2012, 62 (04) :396-427
12345