A HLL-Rankine–Hugoniot Riemann solver for complex non-linear hyperbolic problems

Journal of Computational Physics - Tập 251 - Trang 156-193 - 2013
Capdeville Guy1
1Département de Mécanique des fluides, Ecole Centrale de Nantes, France

Tài liệu tham khảo

Lax, 1971, Sock waves and entropy, 603 Harten, 1983, On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM Rev., 25, 35, 10.1137/1025002 Godunov, 1959, A difference method for the numerical calculation of discontinuous solutions of hydrodynamic equations, Math. Sb., 47, 271 Einfeldt, 1988, On Godunov-type methods for gas dynamics, SIAM J. Numer. Anal., 25, 294, 10.1137/0725021 Einfeldt, 1991, On Godunov-type methods near low densities, J. Comput. Phys., 92, 273, 10.1016/0021-9991(91)90211-3 Linde, 2002, A practical, general-purpose, two-state HLL Riemann solver for hyperbolic conservation laws, Int. J. Numer. Meth. Fluids, 40, 391, 10.1002/fld.312 Miyoshi, 2005, A Multi-state HLL approximate Riemann solver for ideal Magnetohydrodynamics, J. Comput. Phys., 208, 315, 10.1016/j.jcp.2005.02.017 Bouchut, 2007, A multiwave approximate Riemann solver for ideal MHD based on relaxation I – theoretical framework, Numer. Math., 108, 7, 10.1007/s00211-007-0108-8 Bouchut, 2010, A multiwave approximate Riemann solver for ideal MHD based on relaxation II – numerical implementation with 3 and 5 waves, Numer. Math., 115, 647, 10.1007/s00211-010-0289-4 Batten, 1997, On the choice of wavespeeds for the HLLC Riemann solver, SIAM J. Sci. Comput., 18, 1553, 10.1137/S1064827593260140 Toro, 1994, Restoration of the contact surface in the HLL Riemann solver, Shock Waves, 4, 25, 10.1007/BF01414629 Gurski, 2004, An HLLC-type approximate Riemann solver for ideal magnetohydrodynamics, SIAM J. Sci. Comput., 25, 2165, 10.1137/S1064827502407962 Liu, 1994, Weighted essentially non-oscillatory schemes, J. Comput. Phys., 115, 200, 10.1006/jcph.1994.1187 Jiang, 1996, Efficient implementation of weighted WENO schemes, J. Comput. Phys., 126, 202, 10.1006/jcph.1996.0130 Balsara, 2000, Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high-order of accuracy, J. Comput. Phys., 160, 405, 10.1006/jcph.2000.6443 C-W. Shu, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, NASA/CR-97-206253 ICASE Report 97–65 (1997). Levy, 2000, Compact central WENO schemes for multidimensional conservation laws, SIAM J. Sci. Comput., 22, 656, 10.1137/S1064827599359461 Capdeville, 2011, A High-order multi-dimensional HLL-Riemann solver for non-linear Euler equations, J. Comput. Phys., 230, 2915, 10.1016/j.jcp.2010.12.043 Perthame, 1996, On positive preserving finite volume schemes for compressible Euler equations, Numer. Math., 73, 119, 10.1007/s002110050187 T. Linde, P.L. Roe, Robust Euler codes, AIAA-97-2098, 1997, pp. 83–93. Berthon, 2006, Robustness of MUSCL schemes for 2D unstructured meshes, J. Comput. Phys., 218, 495, 10.1016/j.jcp.2006.02.028 Berthon, 2005, Stability of the MUSCL schemes for the Euler equations, Commun. Math. Sci., 3, 133, 10.4310/CMS.2005.v3.n2.a3 Zhang, 2010, On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes, J. Comput. Phys., 229, 8918, 10.1016/j.jcp.2010.08.016 Zhang, 1990, Conjecture on the structure of solutions of the Riemann problem for two-dimensional gas dynamics systems, SIAM J. Math. Anal., 21, 593, 10.1137/0521032 C.W. Schulz-Rinne, J.P. Collins, H.M. Glaz, Numerical solution of the Riemann problem for two-dimensional gas dynamics, SIAM J. Sci. Comput. 14 (6) (1993) 1394–1414. Shi, 2003, Resolution of high-order WENO schemes for complicated flow structures, J. Comput. Phys., 186, 690, 10.1016/S0021-9991(03)00094-9 Woodward, 1984, The numerical simulation of two-dimensional fluid flow with strong shocks, J. Comput. Phys., 54, 115, 10.1016/0021-9991(84)90142-6 Cockburn, 1998, The Runge–Kutta discontinuous galerkin method for conservation laws V, J. Comput. Phys., 141, 199, 10.1006/jcph.1998.5892 Toro, 1997 J. Zhu, J. Qiu, C-W. Shu, M. Dumbser, Runge–Kutta discontinuous Galerkin method using WENO limiters II: unstructured meshes, J. Comput. Phys. 227 (2008) 4330–4353. Shu, 1988, Efficient implementation of essentially non-oscillatory shock capturing schemes, J. Comput. Phys., 77, 439, 10.1016/0021-9991(88)90177-5 Hillier, 1991, Computation of shock wave diffraction at a ninety degrees convex edge, Shock Waves, 89, 10.1007/BF01414904 Quirk, 1994, A contribution to the great Riemann solver debate, Int. J. Numer. Meth. Fluids, 18, 555, 10.1002/fld.1650180603 van Albada, 1982, A comparative study of computational methods in cosmic gas dynamics, Astron. Astroph., 108, 76 Glimm, 1988, The dynamics of bubble growth for Rayleigh–Taylor instability, Phys. Fluids, 31, 447, 10.1063/1.866826 Sharp, 1984, An overview of Rayleigh–Taylor instability, Physica, 12D, 3 Grasso, 2000, Shock-wave-vortex interactions: shock and vortex deformations, and sound production, Theoret. Comput. Fluid Dyn., 13, 421, 10.1007/s001620050121 Qiu, 2002, On the construction, comparison, and local characteristic decomposition for high-order central WENO schemes, J. Comput. Phys., 183, 187, 10.1006/jcph.2002.7191 Zhang, 2010, On maximum-principle-satisfying high-order schemes for scalar conservation laws, J. Comput. Phys., 229, 3091, 10.1016/j.jcp.2009.12.030 Zhang, 2012, Maximum-principle-satisfying and positivity-preserving high-order discontinuous Galerkin schemes for conservation laws on triangular meshes, J. Scient. Comput., 50, 29, 10.1007/s10915-011-9472-8 Balsara, 2012, Self-adjusting, positivity preserving high-order scheme for hydrodynamics and magnetohydrodynamics, J. Comput. Phys., 231, 7504, 10.1016/j.jcp.2012.01.032