A Non Homogeneous Riemann Solver for shallow water and two phase flows

Flow, Turbulence and Combustion

Volumn 76, Issue 4, 2006, Pages 391-402

  Benkhaldoun, Fayssal ^a   Quivy, Laure ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Finite volumes; Non homogeneous systems; SRNHR scheme

Indexed keywords

DIFFUSION; FINITE VOLUME METHOD; NONLINEAR EQUATIONS; PARAMETER ESTIMATION;

FINITE VOLUMES; NON HOMOGENEOUS SYSTEMS; SRNHR SCHEMES;

TWO PHASE FLOW;

EID: 33749003980     PISSN: 13866184     EISSN: 15731987     Source Type: Journal    
DOI: 10.1007/s10494-006-9027-5     Document Type: Conference Paper

References (14)

1. Abgrall, R., Nkonga, B., Saurel, R.: Efficient numerical approximation of compressible multi-material flow for unstructured meshes. Comput. Fluids. An Int. J. 32, 571-605 (2003)
2. Alcrudo, F., Benkhaldoun, F.: Exact solutions to the Riemann problem of the Shallow Water equations with a bottom step. Comput. Fluids 30(6), 643-671 (2001)
3. Audusse, E., Bristeau, M.O.: A well-balanced positivity preserving 'second-order' scheme for shallow water flows on unstructured meshes. J. Comput. Phys. 206(1), 311-333 (2005)
4. Benkhaldoun, F.: Analysis and validation of a new finite volume scheme for nonhomogeneous systems. FVCA3, HPS., Herbin, R., Krner, D. (eds.), pp. 269-276 (2002)
5. Bouchut, F.: Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources. Series: Frontiers in Mathematics, Birkhäuser (2004)
6. Chinnayya, A., Leroux, A.-Y., Seguin, N.: A well-balanced numerical scheme for approximation of the schallo-water equations with topography: the resonance phenomenon. IJFV, http:/averoes.math.univ-paris13.fr, (2004)
7. Gallouët, T., Hérard, J.-M., Seguin, N.: Some approximate Godunov schemes to compute Shallow-Water equations with topography. Comput. Fluids 32(4), 479-513 (2003)
8. Ghidaglia, J.M., Kumbaro, A., Le Coq, G.: On the numerical solution to two fluid models via a cell centered finite volume method. Eur. J. Mech. B. Fluids 841-867 (2001)
9. Leveque, R.J.: Numerical methods for conservation laws. Lectures in Mathematics ETH Zurich, Birkhauser Verlag, p 214 (1992)
10. Mohamed, K.: Un schéma de flux à deux pas pour la simulations numérique en volumes finis de systémes non homogànes. PhD Thesis, Université Paris XIII (2005)
11. Ransom, V.H.: Numerical benchmark tests. In: Hewitt, G.F., Delhaye, J.M., Zuber, N. (eds.), Multiphase Science and Technology, 3. Hemisphere Publishing Corporation (1987)
12. Roe, P.L.: Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43(2), 357-372 (1981)
13. Vazquez, M.E.: Improved treatment of source terms in upwind schemes for the Shallow Water equations in channels with irregular geometry. J. Comput. Phys. 148, 497-526 (1999)
14. Xing, Y., Shu, C.-W.: High order finite difference WENO schemes with the exact conservation property for the Shallow Water equations. J. Comput. Phys. 208(1), 206-227 (2005)