Relativistic MHD with adaptive mesh refinement

Classical and Quantum Gravity

Volumn 23, Issue 22, 2006, Pages

  Anderson, Matthew ^a   Hirschmann, Eric W ^b   Liebling, Steven L ^c   Neilsen, David ^b  

^a LOUISIANA STATE UNIVERSITY   (United States)

^b Brigham Young University   (United States)

^c LONG ISLAND UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33846125631     PISSN: 02649381     EISSN: 13616382     Source Type: Journal    
DOI: 10.1088/0264-9381/23/22/025     Document Type: Article

References (58)

1. Wilson J R 1975 Some magnetic effects in stellar collapse and accretion Ann. N. Y. Acad. Sci. 262 123-32
2. Koide S, Meier D L, Shibata K and Kudoh T 2000 General relativistic simulations of early jet formation in a rapidly rotating black hole magnetosphere Astrophys. J. 536 668
3. De Villiers J-P and Hawley J F 2003 A numerical method for general relativistic magnetohydrodynamics Astrophys. J. 589 458
4. Gammie C F, McKinney J C and Tóth G 2003 HARM: A numerical scheme for general relativistic magnetohydrodynamics Astrophys. J. 589 444
5. Baumgarte T W and Shapiro S L 2003 Collapse of a magnetized star to a black hole Astrophys. J. 585 930-47
6. Komissarov S S 2004 General relativistic magnetohydrodynamic simulations of monopole magnetospheres of black holes Mon. Not. R. Astron. Soc. 350 1431
7. Antón L, Zanotti O, Miralles J A, Martí J M, Ibáñez J M, Font J A and Pons J A 2006 Numerical 3+1 general relativistic magnetohydrodynamics a local characteristic approach Astrophys. J. 637 296
8. Anninos P, Fragile P C and Salmonson J D 2005 COSMOS++: Relativistic magnetohydrodynamics on unstructured grids with local adaptive refinement Astrophys. J. 635 723-40
9. Duez M D, Liu Y T, Shapiro S L and Stephens B C 2005 Relativistic magnetohydrodynamics in dynamical spacetimes: numerical methods and tests Phys. Rev. D. 72 024029
10. Shibata M and Sekiguchi Y I 2005 Magnetohydrodynamics in full general relativity: formulation and tests Phys. Rev. D. 72 044014
11. Balsara D S 2001 Total variation diminishing scheme for relativistic magnetohydrodynamics Astrophys. J. Suppl. 132 83-101
12. Gombosi T I, De Zeeuw D L, Groth C P T and Powell K G 2000 Magnetospheric configuration for Parker-spiral IMF conditions: results of a 3d AMR MHD simulation Adv. Space Res. 26 139-49
13. Gombosi T I, Tóth G, De Zeeuw D L, Powell K G and Stout Q F 2001 Adaptive mesh refinement MHD for global simulations Proc. ISSS 6 1-8
14. Neilsen D, Hirschmann E W and Millward R S 2006 Relativistic MHD and black hole excision: formulation and initial tests Class. Quantum Grav. 23 S505-27
15. Arturo L-S, Font J A, Ibanez J M and Marti J M 2004 Assessment of a high-resolution central scheme for the solution of the relativistic hydrodynamics equations Astron. Astrophys. 428 703-15
16. Shibata M and Font J A 2005 Robustness of a high-resolution central scheme for hydrodynamic simulations in full general relativity Phys. Rev. D 72 047501
17. Motl P 2006 Introducing Flow-er: a hydrodynamics code for relativistic and Newtonian flows April 2006 APS meeting; slides at http://charybdis.phys.lsu. edu/patrickmotl/
18. Dedner A, Kemm F, Kröner D, Munz C-D, Schnitzer T and Wesenberg M 2002 Hyperbolic divergence cleaning for the MHD equations J. Comput. Phys. 175 645
19. Berger M J and Oliger J 1984 Adaptive mesh refinement for hyperbolic partial differential equations J. Comput. Phys. 53 484
20. Lehner L, Liebling S L and Reula O 2006 AMR, stability and higher accuracy Class. Quantum Grav. 23 S421-46 (Preprint gr-qc/0510111)
21. Shu C-W and Osher S 1988 Efficient implementation of essentially non-oscillatory shock-capturing schemes J. Comput. Phys. 77 439-71
22. Baumgarte T W and Shapiro S L 2003 General relativistic MHD for the numerical construction of dynamical spacetimes Astrophys. J. 585 921-9
23. Sloan J and Smarr L L 1985 Numerical Astrophysics (London: Jones and Bartlett) p 52
24. Evans C R and Hawley J F 1988 Simulation of magnetohydrodynamic flows-a constrained transport method Astrophys. J. 332 659
25. Zhang X H 1989 3+1 formulation of general-relativistic perfect magnetohydrodynamics Phys. Rev. D 39 2933
26. Anile A M 1989 Relativistic Fluids and Magneto-Ffluids (Cambridge: Cambridge University Press)
27. Komissarov S S 1999 Godunov-type scheme for relativistic magnetohydrodynamic Mon. Not. R. Astron. Soc. 303 343
28. Del Zanna L, Bucciantini N and Londrillo P 2003 An efficient shock-capturing central-type scheme for multidimensional relativistic flows: II. Magnetohydrodynamics Astron. Astrophys. 400 397-414
29. Leismann T, Antón L, Aloy M A, Müller E, Martí J M, Miralles J A and Ibáñez J M 2005 Relativistic mhd simulations of extragalactic jets Astron. Astrophys. 436 503-26
30. Liu X-D and Osher S 1998 Convex ENO high order multi-dimensional schemes without field by field decomposition or staggered grids J. Comput. Phys. 142 304-30
31. Del Zanna L and Bucciantini N 2002 An efficient shock-capturing central-type scheme for multidimensional relativistic flows: I. Hydrodynamics Astron. Astrophys. 390 1177-86
32. Harten A, Lax P D and van Leer B 1983 On upstream differencing and Godunov-type schemes for hyperbolic conservation laws SIAM Rev. 25 35-61
33. Brackbill J U and Barnes D C 1980 The effect of nonzero ∇ · B on the numerical solution of the magnetohydrodynamic equations J. Comput. Phys. 35 426
34. Brackbill J U 1985 Fluid modeling of magnetized plasmas Space Sci. Rev. 42 153-67
35. Balsara D S 2001 Divergence-free adaptive mesh refinement for magnetohydrodynamics J. Comput. Phys. 174 614
36. Tóth G and Roe P L 2002 Divergence- and curl-preserving prolongation and restriction formulas J. Comput. Phys. 180 736-50
37. Li S and Li H 2000 A novel approach of divergence-free reconstruction for adaptive mesh refinement J. Comput. Phys. 161 605-52
38. Balsara D S 2004 Second-order-accurate schemes for magnetohydrodynamics with divergence-free reconstruction Astrophys. J. Suppl. 151 149-84
39. Tóth G 2000 The ∇ · B = 0 constraint in shock-capturing magnetohydrodynamics codes J. Comput. Phys. 161 605-52
40. Balsara D S and Kim J 2004 A comparison between divergence-cleaning and staggered-mesh formulations for numerical magnetohydrodynamics Astrophys. J. 602 1079-90
41. Brodbeck O, Frittelli S, Hubner P and Reula O A 1999 Einstein's equations with asymptotically stable constraint propagation J. Math. Phys. 40 909
42. Hirschmann E, Lehner L, Neilsen D, Palenzuela C and Reula O in preparation
43. Sebastian K and Shu C-W 2003 Multidomain WENO finite difference method with interpolation at subdomain interfaces J. Sci. Comput. 19 405
44. Liebling S L 2002 The singularity threshold of the nonlinear sigma model using 3d adaptive mesh refinement Phys. Rev. D 66 041703
45. Hornung R, Kohn S, Elliott N, Smith S, Wissink A, Gunney B and Hysom D 2006 SAMRAI home page, http://www.llnl.gov/CASC/SAMRAI/
46. Lawrence Berkeley National Lab, Applied Numerical Algorithms Group 2006 Chombo-infrastructure for adaptive mesh refinement http://seesar.lbl.gov/anag/ chombo/
47. MacNeice P, Olson K, Mobarry C, deFainchtein R and Packer C 2000 PARAMESH: a parallel adaptive mesh refinement community toolkit Comput. Phys. Commun. 126 33-354
48. Deiterding R 2006 AMROC home page, http://amroc.sourceforge.net/
49. Lijewki M, Beckner V and Rendleman C 2006 Boxlib home page, http://seesar.lbl.gov/ccse/Software/index.html
50. Berger M and Rigoutsos I 1991 An algorithm for point clustering and grid generation IEEE Trans. Syst. Man Cybern. 21 1278-86
51. Rendleman C, Beckner V, Lijewski M, Crutchfield W and Bell J 2000 Parallelization of structured, hierarchical adaptive mesh refinement algorithms Comput. Vis. Sci. 3 147-57
52. Pretorius F 2002 Numerical simulations of gravitational collapse PhD Thesis The University of British Columbia
53. Giacomazzo B and Rezzolla L 2006 The exact solution of the Riemann problem in relativistic MHD J. Fluid Mech. 562 223-59
54. Michel F 1972 Accretion of matter by condensed objects Astrophys. Space Sci. 15 153
55. Papadopoulos P and Font J 2000 Relativistic hydrodynamics around black holes and horizon adapted coordinate systems Phys. Rev. D 61 024015
56. Merz H 2006 Scaling performance of CubePM and TVD MHD on blue gene http://www-03.ibm.com/servers/deepcomputing/bluegene
57. Tiglio M, Lehner L and Neilsen D 2004 3d simulations of Einstein's equations: symmetric hyperbolicity, live gauges and dynamic control of the constraints Phys. Rev. D 70 104018
58. Zink B et al 2006 Black hole formation through fragmentation of toroidal polytropes Phys. Rev. Lett. 96 161101