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Finite-Volume Solvers for a Multilayer Saint-Venant System Cover
Open Access
|Oct 2007

References

  1. Audusse E. (2005): A multilayer Saint-Venant model.Discrete and Continuous Dynamical Systems, Series B, Vol. 5, No. 2, pp. 189-214.10.3934/dcdsb.2005.5.189
  2. Audusse E. and Bristeau M.O. (2005): A well-balanced positivity preserving second order scheme for shallow water flows on unstructured meshes.Journal of Computational Physics, Vol. 206, pp. 311-333.10.1016/j.jcp.2004.12.016
  3. Audusse E., Bristeau M.O. and Decoene A. (2006a): 3D free surface flows simulations using a multilayer Saint-Venant model - Comparisons with Navier-Stokes solutions. Proceedings of the 6-th European Conference Numerical Mathematics and Advanced Applications, ENUMATH 2005, Santiago de Compostella, Spain, pp. 181-189.10.1007/978-3-540-34288-5_10
  4. Audusse E., Klein R. and Owinoh A. (2006b): Conservative and well-balanced discretizations for shallow water flows on rotational domains. Proceedings of the 77th Annual Scientific Conference Gesellschaft für Angewandte Mathematik und Mechanik, GAMM 2006, Berlin, Germany.
  5. Audusse E., Bristeau M.O. and Decoene A. (2007): Numerical simulations of 3D free surface flows by a multilayer Saint-Venant model. (submitted).10.1002/fld.1534
  6. Bermudez A. and Vazquez M.E. (1994): Upwind methods for hyperbolic conservation laws with source terms.Computers and Fluids, Vol. 23, No. 8, pp. 1049-1071.10.1016/0045-7930(94)90004-3
  7. Benkhaldoun F., Elmahi I. and Monthe L.A. (1999): Positivity preserving finite volume Roe schemes for transportdiffusion equations.Computer Methods in Applied Mechanics and Engineering, Vol. 178, pp. 215-232.
  8. Bouchut F. (2002): An introduction to finite volume methods for hyperbolic systems of conservation laws with source. Ecole CEA - EDF - INRIA Ecoulements peu profonds à surface libre, Octobre 2002, INRIA Rocquencourt http://www.dma.ens.fr/~fbouchut/publications/fvcours.ps.gz
  9. Bouchut F., Le Sommer J. and Zeitlin V. (2004): Frontal geostrophic adjustment and nonlinear wave phenomena in one dimensional rotating shallow water. Part 2: Highresolution numerical simulations.Journal of Fluid Mechanics, Vol. 513, pp. 35-63.
  10. Bristeau M.O. and Coussin B. (2001): Boundary Conditions for the Shallow Water Equations solved by Kinetic Schemes.INRIA Report, Vol. 4282, http://www.inria.fr/RRRT/RR-4282.html http://www.inria.fr/RRRT/RR-4282.html
  11. Castro M., Macias J. and Pares C. (2001): A Q-scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shallow water system.ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 35, pp. 107-127.
  12. Einfeldt B., Munz C.D., Roe P.L. and Slogreen B. (1991): On Godunov type methods for near low densities.Journal of Computational Physics, Vol. 92, pp. 273-295.10.1016/0021-9991(91)90211-3
  13. Ferrari S. and Saleri F. (2004): A new two-dimensional Shallow Water model including pressure effects and slow varying bottom topography.ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 38, No. 2, pp. 211-234.10.1051/m2an:2004010
  14. George D. (2004): Numerical Approximation of the Nonlinear Shallow Water Equations with Topography and Dry Beds: A Godunov-Type Scheme. M.Sc. Thesis, University of Washington.
  15. Gerbeau J.-F. and Perthame B. (2001): Derivation of Viscous Saint-Venant System for Laminar Shallow Water; Numerical Validation.Discrete and Continuous Dynamical Systems, Ser. B, Vol. 1, No. 1, pp. 89-102.
  16. Godlewski E. and Raviart P.-A. (1996): Numerical Approximation of Hyperbolic Systems of Conservation Laws. New York: Springer-Verlag.10.1007/978-1-4612-0713-9
  17. Godunov S.K. (1959): A difference method for numerical calculation of discontinuous equations of hydrodynamics. Matematicheski Sbornik, pp. 271-300, (in Russian).
  18. Harten A., Lax P.D. and Van Leer B. (1983): On upstream differencing and Godunov-type schemes for hyperbolic conservation laws.SIAM Review, Vol. 25, pp. 35-61.10.1137/1025002
  19. Hervouet J.M. (2003): Hydrodynamique des écoulements à surface libre; Modélisation numérique avec la méthode des éléments finis. Paris: Presses des Ponts et Chaussées, (in French).
  20. Khobalatte B. (1993): Résolution numérique des équations de la mécanique des fluides par des méthides cinétiques. Ph.D. Thesis, Université P. & M. Curie (Paris 6), (in French).
  21. LeVeque R.J. (1992): Numerical Methods for Conservation Laws. Basel: Birkhäuser.10.1007/978-3-0348-8629-1
  22. Lions P.L., Perthame B. and Souganidis P.E. (1996): Existence of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates.Communications on Pure and Applied Mathematics, Vol. 49, No. 6, pp. 599-638.10.1002/(SICI)1097-0312(199606)49:6<;599::AID-CPA2>3.0.CO;2-5
  23. Perthame B. (2002): Kinetic Formulations of Conservation Laws. Oxford: Oxford University Press.
  24. Perthame B. and Simeoni C. (2001): A kinetic scheme for the Saint-Venant system with a source term.Calcolo, Vol. 38, No. 4, pp. 201-231.10.1007/s10092-001-8181-3
  25. Roe P.L. (1981): Approximate Riemann solvers, parameter vectors and difference schemes.Journal of Computational Physics, Vol. 43, pp. 357-372.10.1016/0021-9991(81)90128-5
  26. de Saint-Venant A.J.C. (1971): Théorie du mouvement nonpermanent des eaux, avec application aux crues des rivières et à l'introduction des marées dans leur lit (in French).Comptes Rendus de l'Académie des Sciences, Paris, Vol. 73, pp. 147-154.
DOI: https://doi.org/10.2478/v10006-007-0025-0 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 311 - 320
Published on: Oct 11, 2007
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2007 Emmanuel Audusse, Marie-Odile Bristeau, published by University of Zielona Góra
This work is licensed under the Creative Commons License.

Volume 17 (2007): Issue 3 (September 2007)