High-order accurate discontinuous finite element solution of the 2D Euler equations

被引:501
作者
Bassi, F
Rebay, S
机构
[1] Univ Ancona, Dipartimento Energet, I-60131 Ancona, Italy
[2] Univ Brescia, Dipartimento Ingn Meccan, I-25121 Brescia, Italy
关键词
Euler equations; discontinuous Galerkin; higher order accuracy; boundary conditions;
D O I
10.1006/jcph.1997.5454
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
This paper deals with a high-order accurate discontinuous finite element method for the numerical solution of the Euler equations. The method combines two key ideas which are at the basis of the finite volume and of the finite element method, the physics of wave propagation being accounted for by means of Riemann problems and accuracy being obtained by means of high-order polynomial approximations within elements. We focus our attention on two-dimensional steady-state problems and present higher order accurate (up to fourth-order) discontinuous finite element solutions on unstructured grids of triangles. In particular we show that, in the presence of curved boundaries, a meaningful high-order accurate solution can be obtained only if a corresponding high-order approximation of the geometry is employed. We present numerical solutions of classical test cases computed with linear, quadratic, and cubic elements which illustrate the versatility of the method and the importance of the boundary condition treatment. (C) 1997 Academic Press.
引用
收藏
页码:251 / 285
页数:35
相关论文
共 17 条
[1]  
Barth T. J., 1990, AIAA900013
[2]  
BASSI F, 1993, LECT NOTE PHYS, V414, P245
[3]  
BASSI F, 1995, 4 ICFD C OXF APR 3 6
[4]  
BASSI F, 1993, 3 ICFD C READ APR 19, P345
[5]  
BASSI F, 1996, 14 ICNMFD BANG JUL 1
[6]  
BEY KS, 1991, 911575CP AIAA, P541
[7]   PARALLEL, ADAPTIVE FINITE-ELEMENT METHODS FOR CONSERVATION-LAWS [J].
BISWAS, R ;
DEVINE, KD ;
FLAHERTY, JE .
APPLIED NUMERICAL MATHEMATICS, 1994, 14 (1-3) :255-283
[8]   TVB RUNGE-KUTTA LOCAL PROJECTION DISCONTINUOUS GALERKIN FINITE-ELEMENT METHOD FOR CONSERVATION-LAWS .2. GENERAL FRAMEWORK [J].
COCKBURN, B ;
SHU, CW .
MATHEMATICS OF COMPUTATION, 1989, 52 (186) :411-435
[9]   THE RUNGE-KUTTA LOCAL PROJECTION DISCONTINUOUS GALERKIN FINITE-ELEMENT METHOD FOR CONSERVATION-LAWS .4. THE MULTIDIMENSIONAL CASE [J].
COCKBURN, B ;
HOU, SC ;
SHU, CW .
MATHEMATICS OF COMPUTATION, 1990, 54 (190) :545-581
[10]   TVB RUNGE-KUTTA LOCAL PROJECTION DISCONTINUOUS GALERKIN FINITE-ELEMENT METHOD FOR CONSERVATION-LAWS .3. ONE-DIMENSIONAL SYSTEMS [J].
COCKBURN, B ;
LIN, SY ;
SHU, CW .
JOURNAL OF COMPUTATIONAL PHYSICS, 1989, 84 (01) :90-113