A problem-orientable numerical algorithm for modeling multi-dimensional radiative MHD flows in astrophysics-the hierarchical solution scenario. (English) Zbl 1196.76083

Summary: We present a hierarchical algorithm for the adaptation of numerical solvers in high energy astrophysics.This approach is based on clustering the entries of the global Jacobian in a hierarchical manner that enables employing a variety of solution procedures ranging from a purely explicit time-stepping up to fully implicit schemes.A gradual coupling of the radiative MHD equation with the radiative transfer equation in higher dimensions is possible.Using this approach, it is possible to follow the evolution of strongly time-dependent flows with low/high accuracies and with efficiency comparable to explicit methods, as well as searching quasi-stationary solutions for highly viscous flows.In particular, it is shown that the hierarchical approach is capable of modeling the formation of jets in active galactic nuclei and reproduce the corresponding spectral energy distribution with a reasonable accuracy.


76W05 Magnetohydrodynamics and electrohydrodynamics
76M25 Other numerical methods (fluid mechanics) (MSC2010)
85A25 Radiative transfer in astronomy and astrophysics


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[1] Balbus, S.; Hawley, J., Astrophys. J., 376, (1991)
[2] Beam, R.M.; Warming, R.F., Aiaa, 16, 393, (1978)
[3] Brandt, A., ()
[4] Dongarra, J.; Duff, I.; Sorensen, D.; van der Vorst, H.A., Numerical linear algebra for high-performance computers, (1998), SIAM Philadelphia · Zbl 0914.65014
[5] Felten, J.E.; Rees, M.J., Transfer effects on X-ray lines in optically thick sources, Astronom. astrophys., 21, 139-150, (1972)
[6] Fletcher, C.A.J., Computational techniques for fluid dynamics, vols. I and II, (1988), Springer-Verlag Berlin · Zbl 0706.76001
[7] Font, J.A., Numerical hydrodynamics in general relativity, Living rev. relativity, 3, 1-81, (2000)
[8] Fryxell, B.; Olson, K.; Ricker, P., FLASH: an adaptive mesh hydrodynamics code for modeling astrophysical thermonuclear flashes, Astrophys. J. (suppl.), 131, 273-334, (2000)
[9] Gammie, C.F.; McKinney, J.C.; Tóth, G., HARM: A numerical scheme for general relativistic magnetohydrodynamics, Astrophys. J., 589, 444-457, (2003)
[10] Hirsch, C., Numerical computation of internal and external flows, vols. I and II, (1990), John Wiley & Sons New York
[11] Hujeirat, A.; Papaloizou, J.C.P., Shock formation in accretion columns—a 2D radiative MHD approach, Astronom. astrophys., 340, 593-604, (1998)
[12] Hujeirat, A.; Rannacher, R., On the efficiency and robustness of implicit methods in computational astrophysics, New astron. rev., 45, 425-447, (2001)
[13] Hujeirat, A.; Camenzind, M.; Livio, M., Ion-dominated plasma and the origin of jets in quasars, Astronom. astrophys., 394, L9-L13, (2002)
[14] Hujeirat, A.; Camenzind, M.; Burkert, A., Comptonization and synchrotron emission in 2D accretion flows. I. A new numerical solver for the kompaneets equation, Astronom. astrophys., 386, 757-762, (2002)
[15] Hujeirat, A.; Livio, M.; Camenzind, M.; Burkert, A., A model for the jet-disk connection in BH accreting systems, Astronom. astrophys., 408, 415-430, (2003)
[16] Hujeirat, A., A model for electromagnetic extraction of rotational energy and formation of accretion-powered jets in radio galaxies, Astronom. astrophys., 416, 423-435, (2004)
[17] Hujeirat, A., A method for enhancing the stability and robustness of explicit schemes in CFD, New astron. rev., 2, 3, 173-193, (2004)
[18] Katz, J.A., Nonrelativistic Compton scattering and models of quasars, Astrophys. J., 206, 910-916, (1976)
[19] Iilarinov, A.F.; Sunyaev, R.A., Compton scattering by thermal electrons in X-ray sources, Soviet astr.—astron. J., 16, 45, (1972)
[20] Kley, W., Radiation hydrodynamics of the boundary layer in accretion disks. I. numerical methods, Astronom. astrophys., 208, 98-110, (1989)
[21] Koide, S.; Shibata, K.; Kudoh, T., Relativistic jet formation from black hole magnetized accretion disks: method, tests, and applications of a general relativistic magnetohydrodynamic numerical code, Astrophys. J., 522, 727-752, (1999)
[22] Koide, S.; Shibata, K.; Kudoh, T.; Meier, D.L., Extraction of black hole rotational energy by a magnetic field and the formation of relativistic jets, Science, 195, 1688-1691, (2002)
[23] Komissarov, S.S., A Godunov-type scheme for relativistic magnetohydrodynamics, Mon. not. R. astron. soc., 303, 343-366, (1999)
[24] Levermore, C.D.; Pomraning, G.C., A flux-limited diffusion theory, Astrophys. J., 248, 321-334, (1981)
[25] Mahadevan, R.; Narayan, R.; Yi, I., Harmony of electrons: cyclotron and synchrotron emission by thermal electrons in magnetic fields, Astrophys. J., 465, 327-337, (1996)
[26] R.W. MacCormack, 1985, Current status of numerical solutions of Navier-Stokes equations, AIAA, Paper 81-0110, 1-18
[27] Martí, J.M.; Müller, E., Numerical hydrodynamics in special relativity, Living rev. relativity, 2, 1-100, (1999)
[28] Meier, D.L.; Koide, S.; Uchida, Y., Magnetohydrodynamic production of relativistic jets, Science, 291, 84-92, (2001)
[29] Meier, D., The theory and simulation of relativistic jet formation: towards a unified model for micro- and macroquasars, New astron. rev., 47, 667-672, (2003)
[30] Mihalas, D.; Mihalas, B.W., Foundations of radiation hydrodynamics, (1984), Oxford University Press New York · Zbl 0651.76005
[31] Ouyed, R.; Pudritz, R., Numerical simulation of astrophysical jets from Keplerian disks. II. episodic outflows, Astrophys. J., 484, 794-809, (1997)
[32] Payne, D.G., Time-dependent comptonization—X-ray reverberations, Astrophys. J., 237, 951-963, (1980)
[33] Rybiki, G.B.; Lightman, A.P., Radiation processes, (1979), Wiley-Interscience Publication
[34] Saad, Y.; van der Vorst, H.A., Iterative solution of linear systems in the 20-th century, J. comput. appl. math., 123, 1-33, (2000) · Zbl 0965.65051
[35] Shapiro, S.L.; Lightman, A.P.; Eardley, D.M., A two-temperature accretion disk model for cygnus X-1 structure and spectrum, Astrophys. J., 204, 187-199, (1976)
[36] Stone, J.M.; Norman, M., ZEUS-2D: A radiation magnetohydrodynamics code for astrophysical flows in two space dimensions. I. the hydrodynamic algorithms and tests, Astrophys. J. (suppl.), 80, 791-818, (1992)
[37] Tóth; Keppens, R.; Botchev, M.A., Implicit and semi-implicit schemes in the versatile advection code: numerical tests, Astronom. astrophys., 332, 1159-1170, (1998)
[38] Trottenberg, U., ()
[39] Uchida, Y.; Nakamura, M.; Hirose, S.; Uemura, S., Magnetodynamic formation of jets in accretion process of magnetized mass onto the central gravitator, Ap&ss, 264, 195-212, (1999) · Zbl 0974.85008
[40] De Villiers, J.-P.; Hawley, J.F., A numerical method for general relativistic magnetohydrodynamics, Astrophys. J., 589, 458-480, (2003)
[41] Ziegler, U., NIRVANA+: an adaptive mesh refinement code for gas dynamics and MHD, Comput. phys. comm., 109, 111-123, (1998) · Zbl 0940.76057
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