ENTROPY STABILITY

A collection of selected references on

Entropy conservative and entropy stable approximations
of nonlinear conservation laws and related problems

  • E. Tadmor [MR 86c: 35100] [Abstract]
    Skew self-adjoint form for systems of conservation laws
    Journal of Mathematical Analysis and Applications 103(2) (1984) 428-442.

  • E. Tadmor
    Numerical viscosity and the entropy condition for conservative difference schemes
    Mathematics of Computation 43 (1984), 369-381.

  • E. Tadmor
    A minimum entropy principle in the gas dynamics equations
    Applied Numerical Mathematics 2 (1986), 211-219.

  • E. Tadmor
    Entropy conservative finite element schemes
    "Numerical Methods for Compressible Flows - Finite Difference Element and Volume Techniques",
    Proceedings of the winter annual meeting of the American Society of Mechanical Engineering AMD-Vol. 78
    (T. E. Tezduyar and T.J.R. Hughes, eds.)     (1986), 149-158.

  • E. Tadmor [Abstract]
    Entropy functions for symmetric systems of conservation laws
    Journal of Mathematical Analysis and Applications 122(2) (1987), 355-359.

  • E. Tadmor
    The numerical viscosity of entropy stable schemes for systems of conservation laws. I.
    Mathematics of Computation 49 (1987), 91-103.

  • E. Tadmor [MR 88i:65111]
    The entropy dissipation by numerical viscosity in nonlinear conservative difference schemes
    "Nonlinear Hyperbolic Problems",
    Proceedings of a 1986 Advanced Research Workshop, Lecture Notes in Mathematics, Vol. 1270
    (C. Carasso, P.-A. Raviart and D. Serre, eds.), Springer-Verlag     (1987), 52-63.

  • M. Merriam
    An entropy based approach to nonlinear stability
    NASA Technical Memorandum 101086 (1989).
  • B. Hayes & P. LeFloch,
    Nonclassical shocks and kinetic relations: finite difference schemes
    SIAM J. Numerical Analysis 35(6) (1998) 2169-2194.

  • C. Rhode & P. LeFloch,
    High-order schemes, entropy inequalities, and nonclassical shocks
    SIAM J. Numerical Analysis 37(6) (2000) 2023-2060.

  • C. Chalons & P. LeFloch,
    High-order entropy-conservative schemes and kinetic relations for van der Waals fluids
    J. Computational Physics 168(1) (2001) 184-206.

  • C. Chalons & P. LeFloch,
    A fully discrete scheme for diffusive-dispersive conservation laws
    Numerische Mathematik 89(3) (2001) 493--509.

  • P. LeFloch, J.-M. Mercier & C. Rohde,
    Fully discrete, entropy conservative schemes of arbitrary order
    SIAM J. Numerical Analysis 40(5) (2002) 1968-1992.

  • E. Tadmor
    Entropy stability theory for difference approximations of nonlinear conservation laws and related time dependent problems
    Acta Numerica v. 12 (2003), 451-512.

  • R. Abramov & J. Majda,
    Discrete approximations with additional conserved quantities: deterministic and statistical behavior
    Methods and Applications in Analysis 10(2) (2003) 151--189.

  • E. Tadmor
    On the entropy stability of difference schemes: a comparison principle and a homotopy approach
    ``Hyperbolic Problems: Theory, Numerics, Applications'', vol. I.,
    Proceedings of the 10th International Conference, Osaka, Sep. 2004
    (F. Asukura, H. Aiso, S. Kawashima, A. Matsumura, S. Nishibata & K. Nishihara, eds.)    , Yokohama Publishers, 2006 pp. 195-204.

  • E. Tadmor & W. Zhong
    Entropy stable approximations of Navier-Stokes equations with no artificial numerical viscosity
    J. of Hyperbolic Differential Equations 3(3) (2006) 529-559.

  • P. Roe
    Affordable, entropy-consistent, Euler flux functions (with applications to the carbuncle phenomenon)
    in 11th International Conference on ``Hyperbolic Problems: Theory, Numerics, Applications'', Lyon, July 2006.

  • E. Tadmor & W. Zhong
    Novel entropy stable schemes for 1D and 2D fluid equations
    in ``Hyperbolic Problems: Theory, Numerics, Applications'',
    Proceedings of the 11th International Conference in Lyon, July 2006 (S. Benzoni-Gavage and D. Serre, eds.), Springer 2007, pp. 1111-1120.

  • E. Tadmor & W. Zhong
    Energy-preserving and stable approximations for the two-dimensional shallow water equations
    in "Mathematics and Computation - A Contemporary View",
    Proceedings of the Third Abel Symposium held in Ålesund, Norway May 2006
    (H. Munthe-Kaas & B. Owren eds.), Springer 2008.

  • P. LeFloch & M. Mohammadian
    Why many theories of shock waves are necessary: kinetic functions, equivalent equations, and fourth-order models
    J. Computational Physics 227(8) (2008) 4162-4189.

  • D. Kröner, P. LeFloch & M.-D. Thanh,
    The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section
    Mathematical Modeling & Numerical Analysis 42(3) (2008) 425-442.

  • J. Haink & C. Rohde,
    Local discontinuous-Galerkin schemes for model problems in phase transition theory
    Communications in Computational Physics 4(4) (2008) 860-893.

  • J. M. Mercier,
    Optimally transported schemes: one dimensional case
    Preprint.

  • U. Fjordholm, S. Mishra & E. Tadmor
    Energy preserving and energy stable schemes for the shallow water equations
    in "Foundations of Computational Mathematics", Proc. FoCM held in Hong Kong 2008 (F. Cucker, A. Pinkus & M. Todd, eds), London Math. Soc. Lecture Notes Ser. 363, 2009 pp. 93-139.

  • K. Kitamura, P. Roe & F. Ismail
    Evaluation of Euler fluxes for hypersomic flow computations
    AIAA 47(1) (2009) 44-53.

  • B. Sjogreen & H. Yee
    On skew-symmetric splitting and entropy conservation for the Euler Equations
    ENUMATH (2009).