Free Access
Volume 54, Number 2, March-April 2020
Page(s) 373 - 389
Published online 12 February 2020
  1. F. Chalot, T.J.R. Hughes and F. Shakib, Symmetrization of conservation laws with entropy for high-temperature hypersonic computations. Comput. Syst. Eng. 1 (1990) 495–521. [CrossRef] [Google Scholar]
  2. M.O. Delchini, J.C. Ragusa and R.A. Berry, Viscous regularization for the non-equilibrium seven-equation two-phase flow model. J. Sci. Comput. 69 (2016) 764–804. [Google Scholar]
  3. M.O. Delchini, J.C. Ragusa and J. Ferguson, Viscous regularization of the full set of nonequilibrium-diffusion Grey Radiation-Hydrodynamic equations. Int. J. Numer. Methods Fluids 85 (2017) 30–47. [Google Scholar]
  4. K.O. Friedrichs and P.D. Lax, Systems of conservation equations with a convex extension. Proc. Nat. Acad. Sci. 68 (1971) 1686–1688. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  5. R. Frolov, An efficient algorithm for the multicomponent compressible Navier-Stokes equations in low- and high-Mach number regimes. Comput. Fluids 178 (2019) 15–40. [Google Scholar]
  6. V. Giovangigli, Multicomponent Flow Modeling. Birkhauser, Boston (1999). [CrossRef] [Google Scholar]
  7. V. Giovangigli and L. Matuszewski, Structure of entropies in dissipative multicomponent fluids. Kin. Rel. Models 6 (2013) 373–406. [CrossRef] [Google Scholar]
  8. S.K. Godunov, A difference scheme for numerical computation of discontinuous solutions of equations of fluid dynamics. Math. Sbornik 47 (1959) 271–306. [Google Scholar]
  9. A. Gouasmi, K.D. Duraisamy and S.M. Murman, Formulation of entropy-stable schemes for the compressible multicomponent Euler equations. SIAM J. Appl. Math.. Preprint arxiv:1904.00972v2 2019). [Google Scholar]
  10. J.L. Guermond and B. Popov, Viscous regularization of the Euler equations and entropy principles. SIAM J. Appl. Math. 74 (2014) 284–305. [Google Scholar]
  11. J.L. Guermond and B. Popov, Invariant domain and first-order continuous finite element approximation for hyperbolic systems. SIAM J. Numer. Anal. 54 (2016) 2466–2489. [Google Scholar]
  12. J.L. Guermond and B. Popov, Fast estimation from above of the maximum wave speed in the Riemann problem for the Euler equations. J. Comput. Phys. 328 (2016) 908–926. [Google Scholar]
  13. J.L. Guermond, M. Nazarov, B. Popov and I. Tomas, Second-order invariant domain preserving approximation of the Euler equations using convex limiting. SIAM J. Sci. Comput. 40 (2018) 3211–3239. [Google Scholar]
  14. J.-L. Guermond, B. Popov and I. Tomas, Invariant domain preserving discretization-independent schemes and convex limiting for hyperbolic systems. Comput. Methods Appl. Mech. Eng. 347 (2019) 143–175. [Google Scholar]
  15. A. Harten, P.D. Lax and B. Van Leer, On upstream differencing and godunov-type schemes for hyperbolic conservation laws. SIAM Rev. 25 (1983) 35–61. [CrossRef] [MathSciNet] [Google Scholar]
  16. A. Harten, On the symmetric form of systems of conservation laws with entropy. J. Comput. Phys. 49 (1983) 151–164. [Google Scholar]
  17. A. Harten, P.D. Lax, C.D. Levermore and W.J. Morokoff, Convex entropies and hyperbolicity for general Euler equations. SIAM J. Numer. Anal. 33 (1998) 2117–2127. [Google Scholar]
  18. D. Kroner, P.G. LeFloch and M. Thanh, The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section. ESAIM: M2AN 42 (2008) 425–442. [CrossRef] [EDP Sciences] [Google Scholar]
  19. S.N. Krushkov, First-order quasilinear equations in several independent variables. Math. USSR-Sbornik 10 (1970) 217. [CrossRef] [Google Scholar]
  20. P.D. Lax, Hyperbolic systems of conservation laws II. Commun. Pure Appl. Math. 10 (1957) 537–566. [Google Scholar]
  21. P.D. Lax, Shock waves and entropy, edited by E. Zarantonello. In: Contributions to Nonlinear Functional Analysis. Academia Press, New York (1971) 603–634. [CrossRef] [Google Scholar]
  22. Y. Lv and M. Ihme, Entropy-bounded discontinuous Galerkin scheme for Euler equations. J. Comput. Phys. 295 (2015) 715–773. [Google Scholar]
  23. M.S. Mock, Systems of conservation laws of mixed type. J. Differ. Equ. 70 (1980) 70–88. [Google Scholar]
  24. E. Tadmor, Skew-Self adjoint form for systems of conservation laws. J. Math. Anal. App. 103 (1984) 428–442. [CrossRef] [MathSciNet] [Google Scholar]
  25. E. Tadmor, Numerical viscosity and the entropy condition for conservative difference schemes. Math. Comput. 43 (1984) 369–381. [Google Scholar]
  26. E. Tadmor, A minimum entropy principle in the gas dynamics equations. Appl. Numer. Math. 2 (1986) 211–219. [Google Scholar]
  27. E. Tadmor, The numerical viscosity of entropy stable schemes for systems of conservation laws I. Math. Comput. 49 (1987) 91–103. [Google Scholar]
  28. E.F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction, 3rd edition. Springer, Berlin (2009). [CrossRef] [Google Scholar]
  29. X. Zhang and C.-W. Shu, A minimum entropy principle of high order schemes for gas dynamics equations. Numer. Math. 121 (2012) 545–563. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you