Existence and nonexistence of TV bounds for scalar conservation laws with discontinuous flux, Communications on Pure and Applied Mathematics, vol.38, issue.2, pp.84-0115, 2011. ,
DOI : 10.1002/cpa.20346
Conservation law with discontinuous flux, Journal of Mathematics of Kyoto University, vol.43, issue.1, pp.27-70, 2003. ,
DOI : 10.1215/kjm/1250283740
Application of the DFLU flux to Hamilton-Jacobi equations with discontinuous Hamiltonians ,
Godunov-Type Methods for Conservation Laws with a Flux Function Discontinuous in Space, SIAM Journal on Numerical Analysis, vol.42, issue.1, pp.42179-208, 2004. ,
DOI : 10.1137/S003614290139562X
OPTIMAL ENTROPY SOLUTIONS FOR CONSERVATION LAWS WITH DISCONTINUOUS FLUX-FUNCTIONS, Journal of Hyperbolic Differential Equations, vol.02, issue.04, pp.783-837, 2005. ,
DOI : 10.1142/S0219891605000622
Monotonization of flux, entropy and numerical schemes for conservation laws, Journal of Mathematical Analysis and Applications, vol.352, issue.1, pp.427-439, 2009. ,
DOI : 10.1016/j.jmaa.2008.05.043
URL : https://hal.archives-ouvertes.fr/inria-00349637
Petroleum Reservoir Simulation, 1979. ,
Upstream differencing for multiphase flow in reservoir simulation, SINUM, pp.28685-696, 1991. ,
Well-posedness in BV t and convergence of a difference scheme for continuous sedimentation in ideal clarifier-thickener units, Numerische Mathematik, vol.97, issue.1, pp.25-65, 2004. ,
DOI : 10.1007/s00211-003-0503-8
A finite element simulator for incompressible two-phase flow, Transp.Porous Media, pp.465-478, 1987. ,
Polymer Floods: A Case Study of Nonlinear Wave Analysis and of Instability Control in Tertiary Oil Recovery, SIAM Journal on Applied Mathematics, vol.48, issue.2, pp.353-373, 1988. ,
DOI : 10.1137/0148018
Solution of the Cauchy Problem for a Conservation Law with a Discontinuous Flux Function, SIAM Journal on Mathematical Analysis, vol.23, issue.3, pp.635-648, 1992. ,
DOI : 10.1137/0523032
The structure of asymptotic states in a singular system of conservation laws, Advances in Applied Mathematics, vol.11, issue.2, pp.11205-219, 1990. ,
DOI : 10.1016/0196-8858(90)90009-N
Numerical calculation of the flux across an interface between two rock types of a porous medium for a two-phase flow, Hyperbolic Problems: Theory, World Scientific, pp.165-177, 1996. ,
A Riemann Solver for a Two-Phase Multicomponent Process, SIAM Journal on Scientific and Statistical Computing, vol.10, issue.5, pp.846-879, 1989. ,
DOI : 10.1137/0910050
The Solution of the Riemann Problem for a Hyperbolic System of Conservation Laws Modeling Polymer Flooding, SIAM Journal on Mathematical Analysis, vol.19, issue.3, pp.541-566, 1988. ,
DOI : 10.1137/0519039
Solving the Buckley-Leverett equation with gravity in a heterogeneous porous medium, Computational Geosciences, vol.3, issue.1, pp.23-48, 1999. ,
DOI : 10.1023/A:1011574824970
Semi-Godunov schemes for general triangular systems of conservation laws, Journal of Engineering Mathematics, vol.173, issue.2, pp.3-4, 2008. ,
DOI : 10.1007/s10665-007-9163-5
Convergence of finite volume schemes for triangular systems of conservation laws, Numerische Mathematik, vol.39, issue.4, pp.559-589, 2009. ,
DOI : 10.1007/s00211-008-0199-x
Well-balanced schemes for conservation laws with source terms based on a local discontinuous flux formulation, Mathematics of Computation, vol.78, issue.265, pp.55-78, 2009. ,
DOI : 10.1090/S0025-5718-08-02117-0
Semi-Godunov schemes for multiphase flows in porous media, Applied Numerical Mathematics, vol.59, issue.9, pp.2322-2336, 2009. ,
DOI : 10.1016/j.apnum.2008.12.019
Towers , L 1 stability for entrolpy solutions of nonlinear degenerate parabolic convection-diffusion equations with discontinuous coefficients, Skr. K. Nor. Videensk, issue.3, pp.1-49, 2003. ,
Stability of a Resonant System of Conservation Laws Modeling Polymer Flow with Gravitation, Journal of Differential Equations, vol.170, issue.2, pp.344-380, 2001. ,
DOI : 10.1006/jdeq.2000.3826
Instability of Buckley-Leverett flow in a heterogeneous medium, Transport in Porous Media, vol.22, issue.3, pp.165-185, 1992. ,
DOI : 10.1007/BF00611965
Systems of conservation laws, Communications on Pure and Applied Mathematics, vol.47, issue.2, pp.217-237, 1960. ,
DOI : 10.1002/cpa.3160130205
On the upstream mobility scheme for two-phase flow in porous media, Computational Geosciences, vol.39, issue.3, pp.105-124, 2010. ,
DOI : 10.1007/s10596-009-9135-0
URL : https://hal.archives-ouvertes.fr/inria-00353627
An analysis of the traffic on highways with changing surface conditions, Mathematical Modelling, vol.9, issue.1, pp.1-11, 1987. ,
DOI : 10.1016/0270-0255(87)90068-6
Non-oscillatory central differencing for hyperbolic conservation laws, Journal of Computational Physics, vol.87, issue.2, pp.408-463, 1990. ,
DOI : 10.1016/0021-9991(90)90260-8
The Application of Fractional Flow Theory to Enhanced Oil Recovery, Society of Petroleum Engineers Journal, vol.20, issue.03, pp.191-205, 1980. ,
DOI : 10.2118/7660-PA
ANALYSIS AND APPROXIMATION OF A SCALAR CONSERVATION LAW WITH A FLUX FUNCTION WITH DISCONTINUOUS COEFFICIENTS, Mathematical Models and Methods in Applied Sciences, vol.13, issue.02, pp.221-257, 2003. ,
DOI : 10.1142/S0218202503002477
URL : https://hal.archives-ouvertes.fr/hal-01376535
Global solution of the cauchy problem for a class of 2 ?? 2 nonstrictly hyperbolic conservation laws, Advances in Applied Mathematics, vol.3, issue.3, pp.335-375, 1982. ,
DOI : 10.1016/S0196-8858(82)80010-9
Riemann Solvers and Numerical Methods for Fluid Dynamics, 1999. ,
MUSTA: A multi-stage numerical flux, Applied Numerical Mathematics, vol.56, issue.10-11, pp.1464-1479, 2006. ,
DOI : 10.1016/j.apnum.2006.03.022
Convergence of a Difference Scheme for Conservation Laws with a Discontinuous Flux, SIAM Journal on Numerical Analysis, vol.38, issue.2, pp.38-681, 2000. ,
DOI : 10.1137/S0036142999363668
A Difference Scheme for Conservation Laws with a Discontinuous Flux: The Nonconvex Case, SIAM Journal on Numerical Analysis, vol.39, issue.4, pp.39-1197, 2001. ,
DOI : 10.1137/S0036142900374974
Convergence and stability of the Lax-Friedrichs scheme for a nonlinear parabolic polymer flooding problem, Advances in Applied Mathematics, vol.11, issue.2, pp.11-220, 1990. ,
DOI : 10.1016/0196-8858(90)90010-V
Convergence of a nonconservative finite difference scheme for a system of hyperbolic conservation laws, Diff. Intgral Eqns, vol.3, issue.5, pp.979-1000, 1990. ,
Existence, Uniqueness, and Continuous Dependence for a System of Hyperbolic Conservation Laws Modeling Polymer Flooding, SIAM Journal on Mathematical Analysis, vol.22, issue.4, pp.905-933, 1991. ,
DOI : 10.1137/0522059
A well posed system of hyperbolic conservation laws, Third International Conference on hyperbolic Problems, pp.888-898, 1990. ,