Fast sweeping methods for hyperbolic systems of conservation laws at steady state

被引:14
作者
Engquist, Bjoern
Froese, Brittany D. [1 ]
Tsai, Yen-Hsi Richard
机构
[1] Univ Texas Austin, Dept Math, Austin, TX 78712 USA
基金
美国国家科学基金会; 加拿大自然科学与工程研究理事会;
关键词
Conservation laws; Hyperbolic equations; Fast sweeping methods; Numerical analysis; HAMILTON-JACOBI EQUATIONS; ESSENTIALLY NONOSCILLATORY SCHEMES; EIKONAL EQUATIONS; WENO SCHEMES; MESHES; FLOW;
D O I
10.1016/j.jcp.2013.08.036
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
Fast sweeping methods have become a useful tool for computing the solutions of static Hamilton-Jacobi equations. By adapting the main idea behind these methods, we describe a new approach for computing steady state solutions to systems of conservation laws. By exploiting the flow of information along characteristics, these fast sweeping methods can compute solutions very efficiently. Furthermore, the methods capture shocks sharply by directly imposing the Rankine-Hugoniot shock conditions. We present convergence analysis and numerics for several one- and two-dimensional examples to illustrate the use and advantages of this approach. (c) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码:316 / 338
页数:23
相关论文
共 32 条
[1]   Construction of second-order accurate monotone and stable residual distribution schemes for steady problems [J].
Abgrall, R ;
Mezine, M .
JOURNAL OF COMPUTATIONAL PHYSICS, 2004, 195 (02) :474-507
[2]   High order fluctuation schemes on triangular meshes [J].
Abgrall, R ;
Roe, PL .
JOURNAL OF SCIENTIFIC COMPUTING, 2003, 19 (1-3) :3-36
[3]  
Bardi M., 1997, SYSTEMS CONTROL FDN
[4]   Transonic shocks and free boundary problems for the full Euler equations in infinite nozzles [J].
Chen, Gui-Qiang ;
Chen, Jun ;
Feldman, Mikhail .
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2007, 88 (02) :191-218
[5]   Lax-Friedrichs fast sweeping methods for steady state problems for hyperbolic conservation laws [J].
Chen, Weitao ;
Chou, Ching-Shan ;
Kao, Chiu-Yen .
JOURNAL OF COMPUTATIONAL PHYSICS, 2013, 234 :452-471
[6]   High order residual distribution conservative finite difference WENO schemes for steady state problems on non-smooth meshes [J].
Chou, CS ;
Shu, CW .
JOURNAL OF COMPUTATIONAL PHYSICS, 2006, 214 (02) :698-724
[7]   A DIRECT EULERIAN MUSCL SCHEME FOR GAS-DYNAMICS [J].
COLELLA, P .
SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1985, 6 (01) :104-117
[8]  
Courant R., 1948, SUPERSONIC FLOW SHOC
[9]   VISCOSITY SOLUTIONS OF HAMILTON-JACOBI EQUATIONS [J].
CRANDALL, MG ;
LIONS, PL .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 277 (01) :1-42
[10]   MULTIPLE STEADY-STATES FOR 1-D TRANSONIC FLOW [J].
EMBID, P ;
GOODMAN, J ;
MAJDA, A .
SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1984, 5 (01) :21-41