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A direct Eulerian GRP scheme for spherically symmetric general relativistic hydrodynamics. (English) Zbl 1419.76468

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
65N08 Finite volume methods for boundary value problems involving PDEs
Software:
GR1D
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References:
[1] M. Ben-Artzi and J. Falcovitz, A second-order Godunov-type scheme for compressible fluid dynamics, J. Comput. Phys., 55 (1984), pp. 1–32. · Zbl 0535.76070
[2] M. Ben-Artzi and J. Falcovitz, Generalized Riemann Problems in Computational Fluid Dynamics, Cambridge University Press, Cambridge, 2003. · Zbl 1017.76001
[3] M. Ben-Artzi and J.Q. Li, Hyperbolic balance laws: Riemann invariants and the generalized Riemann problem, Numer. Math., 106 (2007), pp. 369–425. · Zbl 1123.65082
[4] M. Ben-Artzi, J.Q. Li, and G. Warnecke, A direct Eulerian GRP scheme for compressible fluid flows, J. Comput. Phys., 218 (2006), pp. 19–43. · Zbl 1158.76375
[5] J.A. Font, Numerical hydrodynamics and magnetohydrodynamics in general relativity, Living Rev. Relativity, 11 (2008), p. 7.
[6] E. Gourgoulhon, Simple equations for general relativistic hydrodynamics in spherical symmetry applied to neutron star collapse, Astronom. Astrophys., 252 (1991), pp. 651–663.
[7] J. Groah, J. Smoller, and B. Temple, Shock Wave Interactions in General Relativity, Springer, New York, 2007. · Zbl 1113.83002
[8] F.S. Guzmán, F.D. Lora-Clavijo, and M.D. Morales, Revisiting spherically symmetric relativistic hydrodynamics, Rev. Mex. Fís. E, 58 (2012), pp. 84–98.
[9] E. Han, J.Q. Li, and H.Z. Tang, An adaptive GRP scheme for compressible fluid flows, J. Comput. Phys., 229 (2010), pp. 1448–1466. · Zbl 1329.76205
[10] E. Han, J.Q. Li, and H.Z. Tang, Accuracy of the adaptive GRP scheme and the simulation of 2-D Riemann problems for compressible Euler equations, Commun. Comput. Phys., 10 (2011), 577–606. · Zbl 1373.76130
[11] L.D. Landau and E.M. Lifschitz, Fluid Meshanics, Pergaman Press, Elmsford, NY, 1987.
[12] J.Q. Li and G.X. Chen, The generalized Riemann problem method for the shallow water equations with bottom topography, Internat. J. Numer. Methods Engrg., 65 (2006), pp. 834–862. · Zbl 1178.76249
[13] J.Q. Li, Q.B. Li, and K. Xu, Comparisons of the generalized Riemann solver and the gas-kinetic scheme for inviscid compressible flow simulations, J. Comput. Phys., 230 (2011), pp. 5080–5099. · Zbl 1416.76250
[14] J.Q. Li, T.G. Liu, and Z.F. Sun, Implementation of the GRP scheme for computing radially symmetric compressible fluid flows, J. Comput. Phys., 228 (2009), pp. 5867–5887. · Zbl 1280.76041
[15] T. Li and W.C. Yu, Boundary Value Problem for Quasilinear Hyperbolic Systems, Duke University Press, Durham, NC, 1985.
[16] J.Q. Li and Y.J. Zhang, The adaptive GRP scheme for compressible fluid flows over unstructured meshes, J. Comput. Phys., 242 (2013), pp. 367–386. · Zbl 1311.76091
[17] M. Liebendöerfer, S. Rosswog, and F.-K. Thielemann, An adaptive grid, implicit code for spherically symmetric, general relativistic hydrodynamics in comoving coordinates, Astrophys. J. Suppl., 141 (2002), pp. 229–246.
[18] M. Liebendörfer, O.E.B. Messer, A. Mezzacappa, S.W. Bruenn, C.Y. Cardall, and F.K. Thielemann, A Finite difference representation of neutrino radiation hydrodynamics for spherically symmetric general relativistic supernova simulations, Astrophys. J. Suppl., 150 (2004), pp. 263–316.
[19] J.M. Martí and E. Müller, Numerical hydrodynamics in special relativity, Living Rev. Relativity, 6 (2003), p. 7.
[20] M.M. May and R.H. White, Hydrodynamic calculations of general relativistic collapse, Phys. Rev. D, 141 (1996), pp. 1232–1241.
[21] M.M. May and R.H. White, Stellar dynamics and gravitational collapse, Methods Comput. Phys., 7 (1967), pp. 219–258.
[22] E. O’Connor and C.D. Ott, A new open-source code for spherically symmetric stellar collapse to neutron stars and black holes, Class. Quantum Grav., 27 (2010), 114103. · Zbl 1190.83064
[23] D.H. Park, I. Cho, G. Kang, and H.M. Lee, A fully general relativistic numerical simulation code for spherically symmetric matter, J. Korean Phys. Soc., 62 (2013), pp. 393–405.
[24] J.A. Pons, J.A. Font, J.M. Ibán͂ez, J.M. Martí, and J.A. Miralles, General relativistic hydrodynamics with special relativistic Riemann solvers, Astronom. Astrophys., 339 (1998), pp. 638–642.
[25] J.Z. Qian, J.Q. Li, and S.H. Wang, The generalized Riemann problems for compressible fluid flows: Towards high order, J. Comput. Phys., 259 (2014), pp. 358–389. · Zbl 1349.76379
[26] D. Radice and L. Rezzolla, Discontinuous Galerkin methods for general-relativistic hydrodynamics: Formulation and application to spherically symmetric spacetimes, Phys. Rev. D., 84 (2011), 024010.
[27] J.V. Romero, J.M. Ibán͂ez, J.M. Martí, and J.A. Miralles, A new spherically symmetric general relativistic hydrodynamical code, Astrophys. J, 46 (1996), pp. 839–854.
[28] J. Smoller and B. Temple, Global solutions of the relativistic Euler equations, Comm. Math. Phys., 157 (1993), pp. 67–99. · Zbl 0780.76085
[29] H.Z. Tang and T. Tang, Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws, SIAM J. Numer. Anal., 41 (2003), pp. 487–515. · Zbl 1052.65079
[30] B. Temple and J. Smoller, Expanding wave solutions of the Einstein equations that induce an anomalous acceleration into the Standard Model of Cosmology, Proc. Natl. Acad. Sci. USA, 106 (2009), pp. 14213–14218. · Zbl 1203.83004
[31] Z. Vogler, The Numerical Simulation of General Relativistic Shock Waves by a Locally Inertial Godunov Method Featuring Dynamic Time Dilation, Ph.D. thesis, University of California, Davis, 2010.
[32] Z. Vogler and B. Temple, Simulation of general relativistic shock wave interactions by a locally inertial Godunov method featuring dynamical time dilation, Proc. Roy. Soc. A, 468 (2012), pp. 1865–1883. · Zbl 1364.76247
[33] J.R. Wilson, Numerical study of fluid flow in a Kerr space, Astrophys. J., 173 (1972), pp. 431–438.
[34] J.R. Wilson and G.J. Mathews, Relativistic Numerical Hydrodynamics, Cambridge University Press, Cambridge, 2003. · Zbl 1095.83003
[35] K.L. Wu and H.Z. Tang, Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics, J. Comput. Phys., 256 (2014), pp. 277–307. · Zbl 1349.76408
[36] K.L. Wu and H.Z. Tang, High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics, J. Comput. Phys., 298 (2015), pp. 539–564. · Zbl 1349.76550
[37] K.L. Wu and H.Z. Tang, Admissible states and physical constraints preserving numerical schemes for special relativistic magnetohydrodynamics, Math. Models Methods Appl. Sci., submitted.
[38] K.L. Wu, Z.C. Yang, and H.Z. Tang, A third-order accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics, J. Comput. Phys., 264 (2014), pp. 177–208. · Zbl 1349.76551
[39] K.L. Wu, Z.C. Yang, and H.Z. Tang, A third-order accurate direct Eulerian GRP scheme for one-dimensional relativistic hydrodynamics, East Asian J. Appl. Math., 4 (2014), pp. 95–131. · Zbl 1309.76145
[40] S. Yamada, An implicit Lagrangian code for spherically symmetric general relativistic hydrodynamics with an approximate Riemann solver, Astrophys. J., 475 (1997), pp. 720–739.
[41] Z.C. Yang, P. He, and H.Z. Tang, A direct Eulerian GRP scheme for relativistic hydrodynamics: One-dimensional case, J. Comput. Phys., 230 (2011), pp. 7964–7987. · Zbl 1408.76597
[42] Z.C. Yang and H.Z. Tang, A direct Eulerian GRP scheme for relativistic hydrodynamics: Two-dimensional case, J. Comput. Phys., 231 (2012), pp. 2116–2139. · Zbl 1408.76598
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