EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 48 / No 2 (March-April 2014) ESAIM: M2AN, 48 2 (2014) 583-602 References
Issue
ESAIM: M2AN
Volume 48, Number 2, March-April 2014
Multiscale problems and techniques
Page(s) 583 - 602
DOI https://doi.org/10.1051/m2an/2013105
Published online 20 January 2014
  1. B. Andreianov, M. Bendahmane and K.H. Karlsen, Discrete duality finite volume schemes for doubly nonlinear degenerate hyperbolic-parabolic equations. J. Hyperbolic Differ. Equ. 7 (2010) 1–67. [CrossRef] [MathSciNet] [Google Scholar]
  2. B. Andreianov, F. Boyer and F. Hubert, Discrete duality finite volume schemes for Leray-Lions-type elliptic problems on general 2D meshes. Numer. Methods Partial Differ. Equ. 23 (2007) 145–195. [CrossRef] [MathSciNet] [Google Scholar]
  3. T. Barth and D. Jespersen, The design and application of upwind schemes on unstructured meshes, in AIAA, Aerospace Sciences Meeting, 27 th, Reno, NV (1989). [Google Scholar]
  4. M. Berger, M.J. Aftosmis and S.M. Murman, Analysis of slope limiters on irregular grids, in 43rd AIAA Aerospace Sciences Meeting, volume NAS Technical Report NAS-05-007 (2005). [Google Scholar]
  5. C. Berthon, Stability of the MUSCL schemes for the Euler equations. Commun. Math. Sci. 3 (2005) 133–158. [CrossRef] [Google Scholar]
  6. C. Berthon, Numerical approximations of the 10-moment Gaussian closure. Math. Comput. 75 (2006) 1809–1832. [CrossRef] [Google Scholar]
  7. C. Berthon, Robustness of MUSCL schemes for 2D unstructured meshes. J. Comput. Phys. 218 (2006) 495–509. [CrossRef] [Google Scholar]
  8. F. Bouchut, Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources. Frontiers in Mathematics. Birkhäuser Verlag, Basel (2004). [Google Scholar]
  9. F. Bouchut, C. Bourdarias and B. Perthame, A MUSCL method satisfying all the numerical entropy inequalities. Math. Comput. 65 (1996) 1439–1462. [CrossRef] [Google Scholar]
  10. T. Buffard and S. Clain, Monoslope and multislope MUSCL methods for unstructured meshes. J. Comput. Phys. 229 (2010) 3745–3776. [Google Scholar]
  11. C. Calgaro, E. Chane-Kane, E. Creusé and T. Goudon, L∞-stability of vertex-based MUSCL finite volume schemes on unstructured grids: Simulation of incompressible flows with high density ratios. J. Comput. Phys. 229 (2010) 6027–6046. [CrossRef] [Google Scholar]
  12. C. Calgaro, E. Creusé, T. Goudon and Y. Penel, Positivity-preserving schemes for Euler equations: sharp and practical CFL conditions (2012). preprint. [Google Scholar]
  13. S. Clain and V. Clauzon, L∞ stability of the MUSCL methods. Numerische Mathematik 116 (2010) 31–64. [CrossRef] [MathSciNet] [Google Scholar]
  14. S. Clain, S. Diot and R. Loubère, A high-order finite volume method for hyperbolic systems: Multi-dimensional Optimal Order Detection (MOOD). J. Comput. Phys. (2011). [Google Scholar]
  15. F. Coquel and B. Perthame, Relaxation of Energy and Approximate Riemann Solvers for General Pressure Laws in Fluid Dynamics. SIAM J. Numer. Anal. 35 (1998) 2223–2249. [CrossRef] [MathSciNet] [Google Scholar]
  16. Y. Coudière and F. Hubert, A 3d discrete duality finite volume method for nonlinear elliptic equations. SIAM J. Sci. Comput. 33 (2011) 1739–1764. [Google Scholar]
  17. Y. Coudière, C. Pierre, O. Rousseau and R. Turpault, A 2D/3D discrete duality finite volume scheme. Application to ECG simulation. Int. J. Finite 6 (2009) 24. [Google Scholar]
  18. P.H. Cournède, B. Koobus and A. Dervieux, Positivity statements for a mixed-element-volume scheme on fixed and moving grids. European J. Comput. Mechanics/Revue Européenne de Mécanique Numérique 15 (2006) 767–798. [Google Scholar]
  19. M.S. Darwish and F. Moukalled, Tvd schemes for unstructured grids. International Journal of Heat and Mass Transfer 46 (2003) 599–611. [CrossRef] [Google Scholar]
  20. S. Diot, S. Clain, R. Loubère, Improved Detection Criteria for the Multi-dimensional Optimal Order Detection (MOOD) on unstructured meshes with very high-order polynomials. Comput. Fluids 64 (2012) 43–63. [CrossRef] [Google Scholar]
  21. K. Domelevo and P. Omnes, A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids. Math. Model. Numer. Anal. 39 (2005) 1203–1249. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  22. R. Ghostine, G. Kesserwani, R. Mosé, J. Vazquez and A. Ghenaim, An improvement of classical slope limiters for high-order discontinuous Galerkin method. Internat. J. Numer. Methods Fluids 59 (2009) 423–442. [CrossRef] [MathSciNet] [Google Scholar]
  23. E. Godlewski and P.A. Raviart, Numerical approximation of hyperbolic systems of conservation laws, in vol. 118 of Appl. Math. Sci. Springer-Verlag, New York (1996). [Google Scholar]
  24. A. Harten, P.D. Lax and B. Van Leer, On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Review (1983) 35–61. [Google Scholar]
  25. F. Hermeline, A finite volume method for the approximation of diffusion operators on distorted meshes. J. Comput. Phys. 160 (2000) 481–499. [CrossRef] [MathSciNet] [Google Scholar]
  26. F. Hermeline, Approximation of 2-D and 3-D diffusion operators with variable full tensor coefficients on arbitrary meshes. Comput. Methods Appl. Mech. Engrg. 196 (2007) 2497–2526. [Google Scholar]
  27. M.E. Hubbard, Multidimensional slope limiters for MUSCL-type finite volume schemes on unstructured grids. J. Comput. Phys. 155 (1999) 54–74. [Google Scholar]
  28. B. Keen and S. Karni, A second order kinetic scheme for gas dynamics on arbitrary grids. J. Comput. Phys. 205 (2005) 108–130. [CrossRef] [Google Scholar]
  29. K. Kitamura and E. Shima, Simple and parameter-free second slope limiter for unstructured grid aerodynamic simulations. AIAA J. 50 (2012) 1415–1426. [CrossRef] [Google Scholar]
  30. A. Kurganov and E. Tadmor, Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers. Numer. Methods Partial Differ. Equ. 18 (2002) 584–608. [CrossRef] [Google Scholar]
  31. P.D. Lax, Shock waves and entropy, in Contributions to nonlinear functional analysis (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1971). Academic Press, New York (1971) 603–634. [Google Scholar]
  32. P.D. Lax, Hyperbolic systems of conservation laws and the mathematical theory of shock waves. Conference Board of the Math. Sci. Regional Conference Series Appl. Math. No. 11. Society for Industrial and Applied Mathematics, Philadelphia, Pa. (1973). [Google Scholar]
  33. R.J. LeVeque, Finite volume methods for hyperbolic problems. Cambridge Univ Press (2002). [Google Scholar]
  34. Wanai Li, Yu-Xin Ren, Guodong Lei and Hong Luo, The multi-dimensional limiters for solving hyperbolic conservation laws on unstructured grids. J. Comput. Phys. 230 (2011) 7775–7795. [Google Scholar]
  35. Q. Liang and F. Marche, Numerical resolution of well-balanced shallow water equations with complex source terms. Advances in Water Resources 32 (2009) 873–884. [CrossRef] [Google Scholar]
  36. X.D. Liu, A maximum principle satisfying modification of triangle based adaptive stencils for the solution of scalar hyperbolic conservation laws. SIAM J. Numer. Anal. (1993) 701–716. [Google Scholar]
  37. K. Michalak and C. Ollivier-Gooch, Limiters for unstructured higher-order accurate solutions of the euler equations, in Proc. of the AIAA Forty-sixth Aerospace Sciences Meeting (2008). [Google Scholar]
  38. B. Perthame, Second-order Boltzmann schemes for compressible Euler equations in one and two space dimensions. SIAM J. Numer. Anal. (1992) 1–19. [Google Scholar]
  39. B. Perthame and Y. Qiu, A variant of Van Leer’s method for multidimensional systems of conservation laws. J. Computat. Phys. 112 (1994) 370–381. [CrossRef] [Google Scholar]
  40. B. Perthame and C.W. Shu, On positivity preserving finite volume schemes for Euler equations. Numerische Mathematik 73 (1996) 119–130. [CrossRef] [MathSciNet] [Google Scholar]
  41. J. Shi, Y.T. Zhang and C.W. Shu, Resolution of high order WENO schemes for complicated flow structures. J. Comput. Phys. 186 (2003) 690–696. [CrossRef] [Google Scholar]
  42. C.W. Shu, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. Advanced numerical approximation nonlinear Hyperbolic equations (1998) 325–432. [Google Scholar]
  43. E.F. Toro, Riemann solvers and numerical methods for fluid dynamics: a practical introduction. Springer Verlag (2009). [Google Scholar]
  44. B. Van Leer, Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method. J. Comput. Phys. 32 (1979) 101–136. [Google Scholar]
  45. V. Venkatakrishnan, Convergence to steady state solutions of the euler equations on unstructured grids with limiters. J. Comput. Phys. 118 (1995) 120–130. [Google Scholar]
  46. P. Woodward and P. Colella, The numerical simulation of two-dimensional fluid flow with strong shocks. J. Comput. Phys. 54 (1984) 115–173. [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