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The NIRVANA code: parallel computational MHD with adaptive mesh refinement. (English) Zbl 1197.76102
Summary: I report on a new version of the magnetohydrodynamics code NIRVANA which is targeted at the study of astrophysical problems. The new version allows for distributed-memory simulations supporting adaptive mesh refinement. Numerical algorithms include dissipative terms (viscosity, Ohmic diffusion, thermal heat conduction) in a conservative form. Domain decomposition is preferably block-wise in case of unigrid applications but adopts space-filling curve techniques for adaptive mesh applications with a hierarchical block-structured mesh. The code architecture facilitates workload balancing among processors for arbitrary mesh refinement depths maintaining intra-level data locality via space-filling curve mappings and, at the same time, ensuring inter-level data locality by applying a novel technique called block sharing. This way, it is demonstrated that comparable performance can be achieved for problems with locally highly refined grid. The data transfer between processors extensively utilizes the coarse-granularity concept of parallel computing and makes use of the MPI library. Conservation properties of the numerical method carry over to the parallel framework. In particular, the solenoidality condition for the magnetic field is preserved to roundoff precision applying the constrained transport machinery. This paper has its focus of discussion on implementation details related to the parallelization and on a code performance analysis.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76W05 Magnetohydrodynamics and electrohydrodynamics
Software:
NIRVANA; PARAMESH
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References:
[1] Agertz, O., Mon. not. R. astron., (2006)
[2] Balsara, D.S.; Spicer, D.S., J. comput. phys., 149, 270, (1999)
[3] M. Berger, PhD thesis, Stanford Univ., 1982
[4] Berger, M.; Oliger, J., J. comput. phys., 53, 484, (1984)
[5] Berger, M.; Collela, P., J. comput. phys., 82, 64, (1989)
[6] CHOMBO library
[7] Dahlburg, R.B.; Picone, J.M., Phys. fluids B, 1, 2153, (1989)
[8] Fryxell, B.; Olson, K.; Ricker, P., Apjs, 131, 273, (2000)
[9] Fromang, S.; Hennebelle, P.; Teyssier, R., Astron. astrophys., 457, 371, (2006)
[10] Keppens, R.; Nool, M.; Toth, G.; Goedbloed, J.P., Comput. phys. comm., 153, 317, (2003)
[11] A.M. Khokhlov, Memo 6406-97-7950, Nav. Res. Lab, 1997
[12] Kravtsov, A.V.; Klypin, A.A.; Khokhlov, A.M., Apjs, 111, 73, (1997)
[13] Kurganov, A.; Noelle, S.; Petrova, G., SIAM J. sci. comput., 23, 707, (2001)
[14] Li, S.; Li, H., J. comput. phys., 199, 1, (2004)
[15] MacNeice, P.; Olson, K.M.; Mobarry, C.; de Fainchtein, R.; Packer, C., Comput. phys. comm., 126, 330, (2000)
[16] Matsumoto, T., Publ. astron. soc. Japan, 59, 1, (2007)
[17] Mignone, A.; Bodo, G.; Massaglia, S.; Matsakos, T.; Tesileanu, O.; Zanni, C.; Ferrari, A., Apjs, 170, 228, (2007)
[18] J.J. Quinlan, PhD thesis, Cranfield Inst. Tech., 1991
[19] O’Shea, B.; Bryan, G.; Bordner, J., ()
[20] Parashar, M.; Browne, J.C., ()
[21] M. Parashar, J.C. Browne, presented at HICSS-29, 1996
[22] M. Parashar, J.C. Browne, presented at HiPC, 1995
[23] Sagan, H., Space-filling curves, (1994), Springer-Verlag New York · Zbl 0806.01019
[24] Shu, C.-W., SIAM J. sci. statist. comput., 9, 1073, (1988)
[25] Shu, C.-W.; Osher, S., J. comput. phys., 77, 439, (1988)
[26] Teyssier, R., Astron. astrophys., 385, 337, (2002)
[27] Toth, G., J. comput. phys., 161, 605, (2000)
[28] Ziegler, U., J. comput. phys., 196, 393, (2004)
[29] Ziegler, U., Comput. phys. comm., 170, 153, (2005)
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