Upwinding of the source term at interfaces for Euler equations with high friction

Computers and Mathematics with Applications

Volumn 53, Issue 3-4, 2007, Pages 361-375

  Bouchut, Francois ^a   Ounaissa, Haythem ^a   Perthame, Benoît ^a  

^a ÉCOLE NORMALE SUPÉRIEURE   (France)

Author keywords

Finite volume schemes; Friction term; Multi scale analysis; Source terms; Upwind source at interface

Indexed keywords

DENSITY (SPECIFIC GRAVITY); FLOW OF GASES; FRICTION; MATHEMATICAL MODELS; POROUS MATERIALS; TRANSITION FLOW;

FINITE VOLUME SCHEMES; FRICTION TERMS; MULTI-SCALE ANALYSIS; SOURCE TERMS; UPWIND SOURCE AT INTERFACE (USI);

EULER EQUATIONS;

EID: 34247895700     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2006.02.055     Document Type: Article

References (24)

1. Perthame B., Sougandis P.E., and Lions P.L. Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in eulerian and lagrangian coordinates. Comm. Pure Appl. Math. 49 (1996) 599-638
2. Marcati P. The one-dimensional Darcy's law as the limit of a compressible Euler flow. J. Differential Equations 84 1 (1990) 129-146
3. Roe P.L. Upwind differencing schemes for hyperbolic conservation laws with source terms. In: Carasso C., Raviart P.A., and Serre D. (Eds). Nonlinear Hyperbolic Problems. Lecture Notes in Math. vol. 1270 (1987), Springer-Verlag, Berlin 41-51
4. Greenberg J.M., and LeRoux A.-Y. A well balanced scheme for the numerical processing of source terms in hyperbolic equations. SIAM J. Numer. Anal. 33 (1996) 1-16
5. Gosse L., and LeRoux A.-Y. A well balanced scheme designed for inhomogeneous scalar conservation laws. C.R. Acad. Sci. Paris Sér. I Math. 323 5 (1996) 543-546
6. Bermudez A., and Vasquez M.E. Upwind methods for hyperbolic conservation laws with source terms. Comput. Fluids 23 8 (1994) 1049-1071
7. Vazquez-Cendon M.E. Improved treatment of source terms in upwind schemes for the shallow water equations in channels with regular geometry. J. Comput. Phys. 148 (1999) 497-526
8. Gallouet T., Hérard J.-M., and Seguin N. Some approximate Godunov schemes to compute shallow water equations with topography. Comput. Fluids 32 (2003) 479-513
9. Jin S. A steady state capturing method for hyperbolic systems with geometrical source terms. M2AN Math. Model. Numer. Anal. 35 4 (2001) 631-645
10. Kurganov A., and Levy D. Central-upwind schemes for the Saint-Venant system. M2AN Math. Model. Numer. Anal. 36 3 (2002) 397-425
11. Perthame B., and Simeoni C. A kinetic scheme for the Saint-Venant system with a source term. Calcolo 38 4 (2001) 201-231
12. Audusse E., Bouchut F., Bristeau M.-O., Klein R., and Perthame B. A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM J. Sci. Comput. 25 6 (2004) 2050-2065
13. Golse F., Jin S., and Levermore C.D. The convergence of numerical transfer schemes in diffusive regimes. I. Discrete-ordinate method. SIAM J. Numer. Anal. 36 5 (1999) 1333-1369 Electronic
14. Jin S., Pareschi L., and Toscani G. Uniformly accurate diffusive relaxation schemes for multiscale transport equations. SIAM J. Numer. Anal. 38 3 (2000) 913-936 Electronic
15. Buet C., and Cordier S. An asymptotic preserving scheme for hydrodynamics radiative transfert models. C. R. Acad. Sci. Paris Math. 338 12 (2004) 951-956
16. Gosse L., and Toscani G. Asymptotic-preserving & well-balanced schemes for radiative transfer and the Rosseland approximation. Numer. Math. 98 2 (2004) 223-250
17. Lions P.L., Perthame B., and Tadmor E. A kinetic formulation of multidimensional scalar conservation laws and related equations. J. Amer. Math. Soc. 7 (1994) 169-191
18. LeVêque R.J. Finite volume methods for hyperbolic problems. Cambridge Texts in Applied Mathematics (2002), Cambridge University Press, Cambridge
19. Godlewski E., and Raviart P.-A. Numerical approximation of hyperbolic systems of conservation laws. Applied Mathematical Sciences vol. 118 (1996), Springer-Verlag, New York
20. Bouchut F. Nonlinear stability of finite volume methods for hyperbolic conservation laws, and well-balanced schemes for sources. Frontiers in Mathematics series (2004), Birkhauser. 3-7643-6665-6
21. B. Perthame, C. Simeoni, Convergence of the upwind interface source method for hyperbolic conservation laws, in: T. Hou, E. Tadmor (Eds.) Proc. of Hyp2002, vol. 70
22. Katsaounis Th., and Simeoni C. First and second order error estimates for the upwind source at interface method. Math. Comp. 74 249 (2005) 103-122 Electronic
23. Katsaounis Th., Perthame B., and Simeoni C. Upwinding sources at interfaces in conservation laws. Appl. Math. Lett. 17 3 (2004) 309-316
24. Perthame B. Kinetic Formulations of Conservation Laws (2002), Oxford University Press