An entropy-correction free solver for non-homogeneous Shallow Water Equations

Mathematical Modelling and Numerical Analysis

Volumn 37, Issue 5, 2003, Pages 755-772

  Rebollo, Tomás Chacón ^a   Delgado, Antonio Domínguez ^a   Nieto, Enrique D Fernández ^a  

^a UNIVERSITY OF SEVILLE   (Spain)

Author keywords

Entropy correction; Finite Volume Method; Harten Regularization; Shallow water; Source terms; Upwinding

Indexed keywords

EID: 0344585493     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:2003043     Document Type: Article

References (23)

1. A. Bermudez, A. Dervieux, J.A. Desideri and M.E.V. Cendón, Upwind schemes for the two-dimensional shallow water equations with variable depth using unstructured meshes. Comput. Methods Appl. Mech. Engrg. 155 (1998) 49-72.
2. A. Bermúdez and M.E.V. Cendón, Upwind Methods for Hyperbolic Conservation Laws with Source Terms. Comput. & Fluids 23 (1994) 1049-1071.
3. F. Bouchut, An introduction to finite volume methods for hyperbolic systems of conservation laws with source. Actas Ecole CEA-EDF-INRIA, Free surface geophysical flows, 7-10 Octobre, INRIA Rocquencourt, France (2002).
4. F. Dubois and G. Mehlman, A non-parameterized entropy correction for Roe's approximate Riemann solver. Numer. Math. 73 (1996) 169-208.
5. P. Brufau, Simulación bidimensional de flujos hidrodinámicos transitorios en gemotrías irregulares. Ph.D. thesis, Universidad de Zaragoza (2000).
6. T.C. Rebollo, E.D.F. Nieto and M.G. Mármol, A flux-splitting solver for shallow watter equations with source terms. Int. J. Num. Methods Fluids 42 (2003) 23-55.
7. T.C. Rebollo, A.D. Delgado and E.D.F. Nieto, A family of stable numerical solvers for Shallow Water equations with source terms. Comput. Methods Appl. Mech. Engrg. 192 (2003) 203-225.
8. T. Gallouët, J.-M. Hérard and N. Seguin, Some approximate Godunov schemes to compute shallow-water equations with topography. Comput. & Fluids 32 (2003) 479-513.
9. E. Godlewski and P.A. Raviart, Hyperbolic systems of conservation laws. Math. Appl. (1991).
10. E. Godlewski and P.A. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws. Springer-Verlag (1996).
11. A. Harten, P. Lax and A. Van Leer, On upstream differencing and Godunov-type scheme for hyperbolic conservation laws. SIAM Rev. 25 (1983) 35.
12. S. Jin, A steady-state capturing method for hyperbolic systems with geometrical source terms. ESAIM: M2AN 35 (2001) 631-645.
13. A. Kurganov and D. Levy, Central-upwind schemes for the saint-venant system. ESAIM: M2AN 36 (2002) 397-425.
14. A. Kurganov and E. Tadmor, New High-Resolution Central Schemes for Nonlinear Conservations Laws and Convection-Diffusion Equations. J. Comput. Phys. 160 (2000) 214-282.
15. R.J. Le Veque and H.C. Yee, A study of numerical methods for hyperbolic conservation laws with stiff source terms. J. Comput. Phys. 86 (1990) 187-210.
16. R.J. Le Veque, Balancing Source Terms and Flux Gradients in High-Resolution Godunov Methods: The Quasi-Steady Wave-Propagation Algorithm. J. Comp. Phys. 146 (1998) 346-365.
17. B. Perthame and C. Simeoni, A kinetic scheme for the Saint-Venant system with a source term. Calcolo 38 (2001) 201-231.
18. P.L. Roe, Upwind differencing schemes for hyperbolic conservation laws with source terms, in Nonlinear Hyperbolic Problems, C. Carraso, P.A. Raviart and D. Serre, Eds., Springer-Verlag, Lecture Notes in Math. 1270 (1986) 41-51.
19. E.F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer (1997).
20. M.E.V. Cendon, Estudio de esquemas descentrados para su aplicacion a las leyes de conservación hiperbólicas con términos fuente, Ph.D. thesis, Universidad de Santiago de Compostela (1994).
21. M.E.V. Cendón, Improved Treatment of Source Terms in Upwind Schemes for the Shallow Water Equations in Channels with Irregular Geometry. J. Comp. Phys. 148 (1999) 497-526.
22. J.P. Vila, High-order schemes and entropy condition for nonlinear hyperbolic systems of conservations laws. Math. Comp. 50 (1988) 53-73.
23. J.G. Zhou, D.M. Causon, C.G. Mingham and D.M. Ingram, The Surface Gradient Method for the Treatment of Source Terms in the Sallow-Water Equations. J. Comput. Phys. 168 (2001) 1-25.