- N. Andrianov and G. Warnecke, On the solution to the Riemann problem for the compressible duct flow. SIAM J. Appl. Math. 64 (2004) 878–901. [CrossRef] [MathSciNet]
- E. Audusse, F. Bouchut, M.-O. Bristeau, R. Klein and B. Perthame, A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM J. Sci. Comp. 25 (2004) 2050–2065. [CrossRef] [MathSciNet]
- R. Botchorishvili and O. Pironneau, Finite volume schemes with equilibrium type discretization of source terms for scalar conservation laws. J. Comput. Phys. 187 (2003) 391–427. [CrossRef] [MathSciNet]
- R. Botchorishvili, B. Perthame and A. Vasseur, Equilibrium schemes for scalar conservation laws with stiff sources. Math. Comput. 72 (2003) 131–157.
- F. Bouchut, Nonlinear stability of finite volume methods for hyperbolic conservation laws, and well-balanced schemes for sources, Frontiers in Mathematics series. Birkhäuser (2004).
- R. Courant and K.O. Friedrichs, Supersonic Flow and Shock Waves. John Wiley, New York (1948).
- G. Dal Maso, P.G. LeFloch and F. Murat, Definition and weak stability of nonconservative products. J. Math. Pures Appl. 74 (1995) 483–548. [MathSciNet]
- P. Goatin and P.G. LeFloch, The Riemann problem for a class of resonant nonlinear systems of balance laws. Ann. Inst. H. Poincaré Anal. Non Linéaire 21 (2004) 881–902. [CrossRef] [MathSciNet]
- L. Gosse, A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms. Comp. Math. Appl. 39 (2000) 135–159. [CrossRef] [MathSciNet]
- J.M. Greenberg and A.Y. Leroux, A well-balanced scheme for the numerical processing of source terms in hyperbolic equations. SIAM J. Numer. Anal. 33 (1996) 1–16. [CrossRef] [MathSciNet]
- A. Harten, P.D. Lax, C.D. Levermore and W.J. Morokoff, Convex entropies and hyperbolicity for general Euler equations. SIAM J. Numer. Anal. 35 2117–2127 (1998).
- E. Isaacson and B. Temple, Nonlinear resonance in systems of conservation laws. SIAM J. Appl. Math. 52 (1992) 1260–1278. [CrossRef] [MathSciNet]
- E. Isaacson and B. Temple, Convergence of the 2 x 2 Godunov method for a general resonant nonlinear balance law. SIAM J. Appl. Math. 55 (1995) 625–640. [CrossRef] [MathSciNet]
- D. Kröner and M.D. Thanh, On the Model of Compressible Flows in a Nozzle: Mathematical Analysis and Numerical Methods, in Proc. 10th Intern. Conf. “Hyperbolic Problem: Theory, Numerics, and Applications”, Osaka (2004), Yokohama Publishers (2006) 117–124.
- D. Kröner and M.D. Thanh, Numerical solutions to compressible flows in a nozzle with variable cross-section. SIAM J. Numer. Anal. 43 (2006) 796–824.
- P.G. LeFloch, Entropy weak solutions to nonlinear hyperbolic systems under nonconservative form. Comm. Partial. Diff. Eq. 13 (1988) 669–727. [CrossRef] [MathSciNet]
- P.G. LeFloch, Shock waves for nonlinear hyperbolic systems in nonconservative form. Preprint 593, Institute Math. Appl., Minneapolis (1989).
- P.G. LeFloch, Hyperbolic systems of conservation laws: The theory of classical and non-classical shock waves, Lectures in Mathematics. ETH Zürich, Birkäuser (2002).
- P.G. LeFloch, Graph solutions of nonlinear hyperbolic systems. J. Hyper. Diff. Equ. 1 (2004) 243–289.
- P.G. LeFloch and T.-P. Liu, Existence theory for nonlinear hyperbolic systems in nonconservative form. Forum Math. 5 (1993) 261–280. [CrossRef] [MathSciNet]
- P.G. LeFloch and M.D. Thanh, The Riemann problem for fluid flows in a nozzle with discontinuous cross-section. Comm. Math. Sci. 1 (2003) 763–797.
- P.G. LeFloch and M.D. Thanh, The Riemann problem for the shallow water equations with discontinuous topography. Comm. Math. Sci. 5 (2007) 865–885.
- D. Marchesin and P.J. Paes-Leme, A Riemann problem in gas dynamics with bifurcation. Hyperbolic partial differential equations III. Comput. Math. Appl. (Part A) 12 (1986) 433–455. [MathSciNet]
- E. Tadmor, Skew selfadjoint form for systems of conservation laws. J. Math. Anal. Appl. 103 (1984) 428–442. [CrossRef] [MathSciNet]
- E. Tadmor, A minimum entropy principle in the gas dynamics equations. Appl. Numer. Math. 2 (1986) 211–219. [CrossRef] [MathSciNet]
Volume 42, Number 3, May-June 2008
|Page(s)||425 - 442|
|Published online||03 April 2008|