A kinetic scheme for the Saint-Venant system with a source term

Calcolo

Volumn 38, Issue 4, 2001, Pages 201-231

  Perthame, B ^a   Simeoni, C ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

NUMERICAL ANALYSIS; ONE DIMENSIONAL;

BOTTOM TOPOGRAPHY; KINETIC SCHEME; NUMERICAL SCHEME; ONE-DIMENSIONAL; PROPERTY; SAINT VENANT EQUATION; SAINT-VENANT SYSTEM; SOURCE TERMS; STEADY STATE; STILL WATER;

FINITE VOLUME METHOD;

EID: 0012588539     PISSN: 00080624     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10092-001-8181-3     Document Type: Article

References (24)

1. Audusse, E., Bristeau, M.-O., Perthame, B.: Kinetic schemes for Saint-Venant equations with source terms on unstructured grids. RR-3989. Rocquencourt: INRIA 2000
2. Arvanitis, C., Katsaounis, T., Makridakis, C.: Adaptive finite element relaxation schemes for hyperbolic conservation laws. M2AN Math. Model. Numer. Anal. 35, 17-33 (2001)
3. Bermudez, A., Vasquez, M.E.: Upwind methods for hyperbolic conservation laws with source terms. Comput. & Fluids 23, 1049-1071 (1994)
4. Botchorishvili, R., Perthame, B., Vasseur, A.: Schémas d'equilibre pour les lois de conservation scalaires avec des termes sources raides. RR-3891. Rocquencourt: INRA 2000
5. Dafermos, C.M.: Hyperbolic conservation laws in continuum physics. (Grundlehren Math. Wiss Bd. 325) Berlin: Springer 2000
6. Eymard, R., Gallouët, T., Herbin, R.: Finite volume methods. In: Ciarlet, P.G., Lions, J.L. (eds.): Handbook of numerical analysis. Vol. VII. Amsterdam: North-Holland 2000, pp. 713-1020
7. Gallouët, T., Hérard, J.M., Seguin, N.: Some approximate Godunov schemes to compute shallow-water equations with topography. Comput. & Fluids. To appear
8. Gerbeau, J.F., Perthame, B.: Derivation of viscous Saint-Venant system for laminar shallow water; numerical validation: Discrete Contin. Dyn. Syst. Ser. B 1, 89-102 (2001)
9. Godlewski, E., Raviart, P.-A.: Numerical approximations of hyperbolic systems of conservation laws. (Applied Mathematical Sciences 118) New York: Springer 1996
10. Gosse, L., LeRoux, A. Y.: Un schéma-équilibre adapté aux lois de conservation scalaires non-homogènes. C.R. Acad. Sci. Paris Sér. I Math. 323, 543-546 (1996)
11. Gosse, L.: A priori error estimate for a well-balanced scheme designed for inhomogeneous scalar conservation laws. C.R. Acad. Sci. Paris Sér. I Math. 327, 467-472 (1998)
12. Gosse, L.: A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms. Comput. Math. Appl. 39, 135-159 (2000)
13. Gosse, L.: A well-balanced scheme using non-conservative products designed for hyperbolic systems of conservation laws with source terms. Math. Models Methods Appl. Sci. 11, 339-365
14. Greenberg, J.M., LeRoux, A.Y: A well-balanced scheme for the numerical processing of source terms in hyperbolic equations. SIAM J. Numer. Anal. 33, 1-16 (1996)
15. Jin, S.: A steady-state capturing method for hyperbolic systems with geometrical source terms. M2AN Math. Model. Numer. Anal. 35, 631-646 (2001)
16. Le Veque, R.J.: Numerical methods for conservation laws. (Lectures in Mathematics ETH Zurich) Basel: Birkhäuser 1992
17. Le Veque, R.J.: Balancing source terms and flux gradients in high-resolution Godunov methods: the quasi-steady wave-propagation algorithm. J. Comput. Phys. 146, 346-365 (1998)
18. Lions, P.L., Perthame, B., Tadmor, E.: Kinetic formulation of the isentropic gas dy-namics and p-systems. Commun. Math. Phys. 163, 415-431 (1994)
19. Perthame, B.: An introduction to kinetic schemes for gas dynamics. In: Kröner, D. et al. (eds.): An introduction to recent developments in theory and numerics for conservation laws. /Lect. Notes in Comput. Sci. Eng. 5) Berlin: Springer 1999, pp. 1-27
20. Roe, P.L.: Upwind differencing schemes for hyperbolic conservation laws with source terms. In: Carasso, C. et al. (eds.): Nonlinear hyperbolic problems. (Lect. Notes in Math. 1270) Berlin: Springer 1987, pp. 41-51
21. de Saint-Venant, A.-J.-C.: Théorie du mouvement non-permanent des eaux, avec application aux crues des rivière at à l'introduction des marées dans leur lit. C.R. Acad. Sci. Paris 73, 147-154 (1871)
22. Serre, D.: Systèmes de lois de conservation. I. II. Paris: Diderot 1996
23. Stroud, A.H.: Numerical quadrature and solution of ordinary differential equations. (Applied Mathematical Sciences 10) New York: Springer 1974, pp. 106-122
24. Xu, K.: Unsplitting BGK-type schemes for the shallow water equations. Internat. J. Modern Phys. C 10, 505-516 (1999)