An approximate two-dimensional Riemann solver for hyperbolic systems of conservation laws

Journal of Computational Physics

Volumn 205, Issue 1, 2005, Pages 292-314

  Guinot, Vincent ^a  

^a UNIVERSITÉ DE MONTPELLIER   (France)

Author keywords

Conservation laws; Godunov type schemes; Riemann solver; Shallow water equations; Shock waves; Source term discretization

Indexed keywords

EQUATIONS OF MOTION; PARTIAL DIFFERENTIAL EQUATIONS; PHYSICAL PROPERTIES;

CONSERVATION LAW; DISCRETIZATIONS; GODUNOV-TYPE SCHEMES; HYPERBOLIC SYSTEMS OF CONSERVATION LAWS; RIEMANN SOLVER; SHALLOW WATER EQUATIONS; SHOCK-WAVES; SOURCE TERM DISCRETIZATION; SOURCE TERMS; TWO-DIMENSIONAL;

SHOCK WAVES;

EID: 16844383949     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2004.11.006     Document Type: Article

References (27)

1. J.B. Bell C.N. Dawson G.R. Shubin An unsplit, higher order Godunov method for scalar conservation laws in multiple dimensions J. Comput. Phys. 74 1988 1-24
2. A. Bermudez E. VasquezCendron Upwind methods for hyperbolic conservation laws with source terms Comp. Fluid 23 1994 1049-1071
3. M. Brio A.R. Zakharian G.M. Webb Two-dimensional Riemann solver for Euler equations of gas dynamics J. Comput. Phys. 167 2001 177-195
4. P. Colella Multidimensional upwind methods for hyperbolic conservation laws J. Comput. Phys. 87 1990 171-200
5. M. Crandall A. Majda The method of fractional steps for conservation laws Numer. Math. 34 1980 285-314
6. A. Dadone B. Grossmann Characteristic-based, rotated upwind scheme for the Euler equations AIAA J. 30 1992 2219-2226
7. W. Dai P.R. Woodward Extension of the piecewise parabolic method to multidimensional ideal magnetohydrodynamics J. Comput. Phys. 115 1994 485-514
8. W. Dai P.R. Woodward A second-order unsplit Godunov scheme for two- and three-dimensional Euler equations J. Comput. Phys. 134 1997 261-281
9. A. Daubert O. Graffe Quelques aspects des écoulements presque horizontaux à deux dimensions en plan et non permanents, application aux estuaires La Houille Blanche 8 1967 847-860 (in French)
10. S.F. Davis Simplified second-order Godunov-type methods SIAM J. Sci. Statistic. Comput. 9 1988 445-473
11. P. Garcia-Navarro M.E. Vasquez-Cendron On numerical treatment of the source terms in the shallow water equations Comp. Fluid 29 2000 951-979
12. V. Guinot Linear advection modelling: The issue of divergent flows J. Hydroinform. 2 2000 113-121
13. V. Guinot Riemann solvers and boundary conditions for two-dimensional shallow-water simulations Int. J. Numer. Meth. Fluid 41 2003 1191-1219
14. V. Guinot Godunov-type Schemes: An Introduction for Engineers 2003 Elsevier Amsterdam
15. N. Katopodes T. Strelkoff Two-dimensional shallow-water wave models J. Eng. Mech. Div., ASCE 105 1979 317-334
16. A. Harten P.D. Lax B. van Leer On upstream differencing and Godunov-type schemes for hyperbolic conservation laws SIAM Rev. 25 1983 35-61
17. R.J. LeVeque Wave propagation algorithms for multidimensional hyperbolic systems J. Comput. Phys. 131 1997 327-353
18. R.J. LeVeque High resolution finite volume methods on arbitrary grids via wave propagation J. Comput. Phys. 78 1988 36-63
19. R.J. LeVeque Finite Volume Methods for Hyperbolic Problems 2002 Cambridge University Press Cambridge
20. D.W. Levy K.G. Powell B. Van Leer Use of a rotated Riemann solver for the two-dimensional Euler equations J. Comput. Phys. 106 1993 201-214
21. J. Saltzmann An unsplit 3D upwind method for hyperbolic conservation laws J. Comput. Phys. 115 1994 153-168
22. G. Strang On the construction and comparison of difference schemes SIAM J. Numer. Anal. 5 1968 506-517
23. H. Sauerwein Numerical calculations of multidimensional and unsteady flows by the method of characteristics J. Comput. Phys. 1 1967 406-432
24. H. Sauerwein The method of characteristics for the three-dimensional unsteady magnetofluid dynamics of a multi-component medium J. Fluid Mech. 25 1966 17-41
25. E.F. Toro Riemann Solvers and Numerical Methods for Fluid Dynamics 1999 Springer Berlin
26. E.F. Toro M. Spruce W. Speares Restoration of the contact surface in the HLL-Riemann solver Shock Waves 4 1994 25-34
27. B. Van Leer Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection J. Comput. Phys. 23 1977 276-299