×

zbMATH — the first resource for mathematics

Admissible states and physical-constraints-preserving schemes for relativistic magnetohydrodynamic equations. (English) Zbl 1371.76096

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
76W05 Magnetohydrodynamics and electrohydrodynamics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
Software:
ECHO
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Anderson, M.; Hirschmann, E. W.; Liebling, S. L.; Neilsen, D., Relativistic MHD with adaptive mesh refinement, Class. Quantum Grav., 23, 6503-6524, (2006) · Zbl 1133.83343
[2] Antón, L.; Miralles, J. A.; Martí, J. M.; Ibáñez, J. M.; Aloy, M. A.; Mimica, P., Relativistic magnetohydrodynamics: renormalized eigenvectors and full wave decomposition Riemann solver, Astrophys. J. Suppl. Ser., 188, 1-31, (2010)
[3] Balsara, D. S., Total variation diminishing scheme for relativistic magnetohydrodynamics, Astrophys. J. Suppl. Ser., 132, 83-101, (2001)
[4] Balsara, D. S., Second-order-accurate schemes for magnetohydrodynamics with divergence-free reconstruction, Astrophys. J. Suppl. Ser., 151, 149-184, (2004)
[5] Balsara, D. S., Divergence-free reconstruction of magnetic fields and WENO schemes for magnetohydrodynamics, J. Comput. Phys., 228, 5040-5056, (2009) · Zbl 1280.76030
[6] Balsara, D. S., Self-adjusting, positivity preserving high order schemes for hydrodynamics and magnetohydrodynamics, J. Comput. Phys., 231, 7504-7517, (2012)
[7] Balsara, D. S.; Kim, J., A subluminal relativistic magnetohydrodynamics scheme with ADER-WENO predictor and multidimensional Riemann solver-based corrector, J. Comput. Phys., 312, 357-384, (2016) · Zbl 1351.76157
[8] Borges, R.; Carmona, M.; Costa, B.; Don, W. S., An improved weighted essentially nonoscillatory scheme for hyperbolic conservation laws, J. Comput. Phys., 227, 3101-3211, (2008) · Zbl 1136.65076
[9] Brackbill, J. U.; Barnes, D. C., The effect of nonzero \(####\)B on the numerical solution of the magnetohydrodynamic equations, J. Comput. Phys., 35, 426-430, (1980) · Zbl 0429.76079
[10] Cheng, Y.; Li, F. Y.; Qiu, J. X.; Xu, L. W., Positivity-preserving DG and central DG methods for ideal MHD equations, J. Comput. Phys., 238, 255-280, (2013) · Zbl 1286.76162
[11] Christlieb, A. J.; Liu, Y.; Tang, Q.; Xu, Z. F., Positivity-preserving finite difference weighted ENO schemes with constrained transport for ideal magnetohydrodynamic equations, SIAM J. Sci. Comput., 37, A1825-A1845, (2015) · Zbl 1329.76225
[12] Cissoko, M., Detonation waves in relativistic hydrodynamics, Phys. Rev. D, 45, 1045-1052, (1992)
[13] Cockburn, B.; Hu, S. C.; Shu, C.-W., The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case, Math. Comput., 54, 545-581, (1990) · Zbl 0695.65066
[14] Zanna, L. Del; Bucciantini, N.; Londrillo, P., An efficient shock-capturing central-type scheme for multidimensional relativistic flows II. magnetohydrodynamics, Astron. Astrophys., 400, 397-413, (2003) · Zbl 1222.76122
[15] Zanna, L. Del; Zanotti, O.; Bucciantini, N.; Londrillo, P., ECHO: A Eulerian conservative high-order scheme for general relativistic magnetohydrodynamics and magnetodynamics, Astron. Astrophys., 473, 11-30, (2007)
[16] Evans, C. R.; Hawley, J. F., Simulation of magnetodydrodynamic flows: A constrained transport method, Astrophys. J., 332, 659-677, (1988)
[17] Font, J. A., Numerical hydrodynamics and magnetohydrodynamics in general relativity, Living Rev. Relativ., 11, 7, (2008) · Zbl 1166.83003
[18] Friedrichs, K. O., On the laws of relativistic electro-magneto-fluid dynamics, Commun. Pure Appl. Math., 27, 749-808, (1974) · Zbl 0308.76075
[19] Giacomazzo, B.; Rezzolla, L., The exact solution of the Riemann problem in relativistic magnetohydrodynamics, J. Fluid Mech., 562, 223-259, (2006) · Zbl 1097.76073
[20] Gottlieb, S.; Ketcheson, D. J.; Shu, C.-W., High order strong stability preserving time discretizations, J. Sci. Comput., 38, 251-289, (2009) · Zbl 1203.65135
[21] He, P.; Tang, H. Z., An adaptive moving mesh method for two-dimensional relativistic magnetohydrodynamics, Comput. Fluids, 60, 1-20, (2012) · Zbl 1365.76337
[22] Honkkila, V.; Janhunen, P., HLLC solver for ideal relativistic MHD, J. Comput. Phys., 223, 643-656, (2007) · Zbl 1111.76036
[23] Jonker, L. D., Immersions with semi-definite second fundamental forms, Canad. J. Math., 27, 610-617, (1975) · Zbl 0328.53041
[24] Kim, J.; Balsara, D. S., A stable HLLC Riemann solver for relativistic magnetohydrodynamics, J. Comput. Phys., 270, 634-639, (2014) · Zbl 1349.76618
[25] Komissarov, S. S., A Godunov-type scheme for relativistic magnetohydrodynamics, Mon. Not. Roy. Astron. Soc., 303, 343-366, (1999)
[26] Krivodonova, L.; Xin, J.; Remacle, J.-F.; Chevaugeon, N.; Flaherty, J. E., Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws, Appl. Numer. Math., 48, 323-338, (2004) · Zbl 1038.65096
[27] Li, F. Y.; Shu, C.-W., Locally divergence-free discontinuous Galerkin methods for MHD equations, J. Sci. Comput., 22, 413-442, (2005) · Zbl 1123.76341
[28] Li, F. Y.; Xu, L. W.; Yakovlev, S., Central discontinuous Galerkin methods for ideal MHD equations with the exactly divergence-free magnetic field, J. Comput. Phys., 230, 4828-4847, (2011) · Zbl 1416.76117
[29] Martí, J. M.; Müller, E., Grid-based methods in relativistic hydrodynamics and magnetohydrodynamics, Living Rev. Comput. Astrophys., 1, 3, (2015)
[30] Mignone, A.; Bodo, G., An HLLC Riemann solver for relativistic flows — II. magnetohydrodynamics, Mon. Not. Roy. Astron. Soc., 368, 1040-1054, (2006)
[31] Miyoshi, T.; Kusano, K., A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics, J. Comput. Phys., 208, 315-344, (2005) · Zbl 1114.76378
[32] Newman, W. I.; Hamlin, N. D., Primitive variable determination in conservative relativistic magnetohydrodynamic simulations, SIAM J. Sci. Comput., 36, B661-B683, (2014) · Zbl 1303.83002
[33] Noble, S. C.; Gammie, C. F.; McKinney, J. C.; Zanna, L. D., Primitive variable solvers for conservative general relativistic magnetohydrodynamics, Astrophys. J. Suppl. Ser., 641, 626-637, (2006)
[34] Qamar, S.; Warnecke, G., A high-order kinetic flux-splitting method for the relativistic magnetohydrodynamics, J. Comput. Phys., 205, 182-204, (2005) · Zbl 1087.76090
[35] Qiu, J.; Shu, C.-W., Runge-Kutta discontinuous Galerkin method using WENO limiters, SIAM J. Sci. Comput., 26, 907-929, (2005) · Zbl 1077.65109
[36] Rossmanith, J. A., An unstaggered, high-resolution constrained transport method for magnetohydrodynamic flows, SIAM J. Sci. Comput., 28, 1766-1797, (2006) · Zbl 1344.76092
[37] Tóth, G., The \(\nabla \cdot\)B = 0 constraint in shock-capturing magnetohydrodynamics codes, J. Comput. Phys., 161, 605-652, (2000) · Zbl 0980.76051
[38] van der Holst, B.; Keppens, R.; Meliani, Z., A multidimensional grid-adaptive relativistic magnetofluid code, Comput. Phys. Comm., 179, 617-627, (2008) · Zbl 1197.76085
[39] Wu, K. L., Design of provably physical-constraint-preserving methods for general relativistic hydrodynamics, Phys. Rev. D, 95, 103001, (2017)
[40] Wu, K. L.; Tang, H. Z., High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics, J. Comput. Phys., 298, 539-564, (2015) · Zbl 1349.76550
[41] Wu, K. L.; Tang, H. Z., Physical-constraints-preserving central discontinuous Galerkin methods for special relativistic hydrodynamics with a general equation of state, Astrophys. J. Suppl. Ser., 228, 3, (2017)
[42] Xing, Y.; Zhang, X.; Shu, C.-W., Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations, Adv. Water Res., 33, 1476-1493, (2010)
[43] Yang, H.; Li, F. Y., Stability analysis and error estimates of an exactly divergence-free method for the magnetic induction equations, ESAIM: Math. Model. Numer. Anal., 50, 965-993, (2016) · Zbl 1348.78028
[44] Zanotti, O.; Fambri, F.; Dumbser, M., Solving the relativistic magnetohydrodynamics equations with ADER discontinuous Galerkin methods, a posteriori subcell limiting and adaptive mesh refinement, Mon. Not. Roy. Astron. Soc., 452, 3010-3029, (2015)
[45] Zhang, X.; Shu, C.-W., On maximum-principle-satisfying high order schemes for scalar conservation laws, J. Comput. Phys., 229, 3091-3120, (2010) · Zbl 1187.65096
[46] Zhang, X.; Shu, C.-W., On positivity-preserving high-order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes, J. Comput. Phys., 229, 8918-8934, (2010) · Zbl 1282.76128
[47] Zhang, X.; Shu, C.-W., Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments, Proc. Roy. Soc. A, 467, 2752-2776, (2011) · Zbl 1222.65107
[48] Zhao, J.; Tang, H. Z., Runge-Kutta discontinuous Galerkin methods for the special relativistic magnetohydrodynamics, J. Comput. Phys., 343, 33-72, (2017) · Zbl 1380.76048
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.