DIMEX Runge-Kutta finite volume methods for multidimensional hyperbolic systems

Mathematics and Computers in Simulation

Volumn 75, Issue 5-6, 2007, Pages 141-160

  Bertolazzi, Enrico ^a   Manzini, Gianmarco ^b  

^a UNIVERSITY OF TRENTO   (Italy)

^b CNR   (Italy)

Author keywords

Finite volume; Implicit explicit; M matrix; Partial differential equation; Runge Kutta

Indexed keywords

FINITE VOLUME METHOD; GRID COMPUTING; MATRIX ALGEBRA; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; POLYNOMIALS;

FLUX FUNCTIONS; MULTIDIMENSIONAL HYPERBOLIC SYSTEMS; NUMERICAL STIFFNESS;

RUNGE KUTTA METHODS;

EID: 34547956814     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2006.12.002     Document Type: Article

References (29)

1. Ascher U.M., Ruuth S.J., and Spiteri R.J. Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations. Appl. Numer. Math. 25 2-3 (1997) 151-167 (special issue on time integration (Amsterdam, 1996)).
2. Ascher U.M., Ruuth S.J., and Wetton B.T.R. Implicit-explicit methods for time-dependent partial differential equations. SIAM J. Numer. Anal. 32 3 (1995) 797-823
3. Bergamaschi L., Mantica S., and Manzini G. A mixed finite element-finite volume formulation of the black-oil model, SIAM. J. Sci. Comput. 20 3 (1998) 970-997
4. Berman A., and Plemmons R.J. Nonnegative Matrices in the Mathematical Sciences (1994), SIAM, Philadelphia (republished in "Classics in Applied Mathematics").
5. Bertolazzi E., and Manzini G. High-order IMEX-RK finite volume methods for multidimensional hyperbolic systems. ENUMATH 2001 Conference, ENUMATH (2001) 35-44
6. Bertolazzi E., and Manzini G. Algorithm 817 P2MESH: generic object-oriented interface between 2-D unstructured meshes and FEM/FVM-based PDE solvers. ACM TOMS 28 1 (2002) 101-132
7. Bertolazzi E., and Manzini G. A second-order maximum principle preserving finite volume method for steady convection-diffusion problems. SIAM J. Numer. Anal. 43 5 (2006) 2172-2199
8. Bertolazzi E., and Manzini G. A finite volume method for transport of contaminants in porous media. Appl. Numer. Math. 49 3-4 (2004) 291-305
9. Bertolazzi E., and Manzini G. A cell-centered second-order accurate finite volume method for convection-diffusion problems on unstructured meshes. Math. Models Methods Appl. Sci. 14 8 (2004) 1235-1260
10. Bertolazzi E., and Manzini G. Limiting strategies for polynomial reconstructions in the finite volume approximation of the linear advection equation. Appl. Numer. Math. 49 3-4 (2004) 277-289
11. Bertolazzi E., and Manzini G. A triangle-based unstructured finite volume method for chemically reactive hypersonic flows. J. Comput. Phys. 166 (2001) 84-115
12. Einfeldt B. On Godunov-type methods for gas dynamics. SIAM J. Numer. Anal. 25 2 (1988) 294-318
13. Einfeldt B., Munz C.-D., Roe P.L., and Sjögreen B. On Godunov-type methods near low densities. J. Comput. Phys. 92 2 (1991) 273-295
14. Funderlic R.E., and Plemmons R.J. LU decomposition of M-matrices by elimination without pivoting. Lin. Algebra Appl. 41 (1981) 99-110
15. Horvath Z. Positivity of Runge-Kutta and diagonally split Runge-Kutta methods. Appl. Numer. Math. 28 (1998) 309-326
16. Kurganov A., and Petrova G. Central schemes and contact discontinuities. Math. Model. Numer. Anal. 34 6 (2000) 1259-1275
17. Kurganov A., and Tadmor E. New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations. J. Comput. Phys. 160 1 (2000) 241-282
18. Leer B.V. Towards the ultimate conservative difference scheme. J. Comput. Phys. 32 (1979) 101-136
19. Leer B.V. Flux-vector splitting for the Euler equations. Lecture Notes Phys. 170 (1982) 507-512
20. Liotta S.F., Romano V., and Russo G. Central schemes for balance laws of relaxation type. SIAM J. Numer. Anal. 38 4 (2000) 1337-1356
21. +. J. Comput. Phys. 129 2 (1996) 364-382
22. Manzini G., and Ferraris S. Mass-conservative finite-volumes on unstructured grids for the Richards' equation. Adv. Water Res. 27 (2004) 1199-1215
23. Meijerink J.A., and van der Vorst H.A. An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix. Math. Comput. 31 137 (1977) 148-162
24. Neumann M. On the Schur complement and the LU-factorization of a matrix. Lin. Multilin. Algebra 9 4 (1980/81) 241-254
25. Ruggeri T. Galilean invariance and entropy principle for systems of balance laws. The structure of extended thermodynamics. Contin. Mech. Thermodyn. 1 1 (1989) 3-20
26. Shu C.-W., and Osher S. Efficient implementation of essentially nonoscillatory shock-capturing schemes. II. J. Comput. Phys. 83 1 (1989) 32-78
27. Steger J.L., and Warming R.F. Flux-vector splitting of the inviscid gas dynamic equations with application to finite-difference methods. J. Comput. Phys. 40 (1981) 263-293
28. ∞. Lin. Algebra Appl. 14 3 (1976) 211-217
29. Wada Y., and Liou M.-S. An accurate and robust flux splitting scheme for shock and contact discontinuities. SIAM J. Sci. Comput. 18 3 (1997) 633-657