FLIP MHD: A particle-in-cell method for magnetohydrodynamics. (English) Zbl 0726.76078
Summary: The fluid-implicit-particle method, FLIP, is extended to magnetohydrodynamic (MHD) flow in two or three dimensions. FLIP-MHD incorporates a Lagrangian representation of the field and is shown to preserve contact discontinuities, to preserve the Galilean invariance of the MHD flow equation, and to give a grid magnetic Reynolds number up to 16. The conservation of mass, momentum, magnetic flux and energy are demonstrated by analysis and numerical examples. Results from numerical calculation in two dimensions of the convection of a contact discontinuity, Rayleigh-Taylor unstable flow, and a confined eddy are presented.
MSC:
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
Keywords:
particle-in-cell method; fluid-implicit-particle method; FLIP-MHD; Lagrangian representation; Galilean invariance of the MHD flow equation; Rayleigh-Taylor unstable flow; confined eddyReferences:
| [1] | Brackbill, J. U.; Ruppel, H. M., J. Comput. Phys., 65, 314 (1986) · Zbl 0592.76090 |
| [2] | Harlow, F. H., Methods Comput. Phys., 3, 319 (1963) |
| [3] | Monaghan, J. J., Comput. Phys. Rep., 3, 71 (1985) |
| [4] | Brackbill, J. U., Comput Phys. Commun., 48, 25 (1988) |
| [5] | Brackbill, J. U., Comput. Phys. Commun., 47, 1 (1987) · Zbl 0673.76085 |
| [6] | Gottlieb, D.; Orszag, S. A., Numerical Analysis of Spectral Methods, ((1977), Soc. Indus. Appl. Math: Soc. Indus. Appl. Math Philadelphia), 135 · Zbl 0412.65058 |
| [7] | Butler, T. D., Phys. Fluids, 12, 1904 (1969) |
| [8] | Brunel, F., J. Comput. Phys., 43, 268 (1981) |
| [9] | Brackbill, J. U.; Barnes, D. C., J. Comput. Phys., 35, 426 (1980) · Zbl 0429.76079 |
| [10] | Deboor, Carl, A Practical Guide to Splines (1978), Springer-Verlag: Springer-Verlag New York · Zbl 0406.41003 |
| [11] | Birdsall, C. K.; Langdon, A. B., Plasma Physics via Computer Simulation (1985), McGraw-Hill: McGraw-Hill New York |
| [12] | Hockney, R. W.; Eastwood, J. W., Computer Simulation Using Particles (1981), McGraw-Hill: McGraw-Hill New York · Zbl 0662.76002 |
| [13] | Brackbill, J. U., Methods Comput. Phys., 16, 1 (1976) |
| [14] | Brackbill, J. U., Fundamentals of Numerical Magnetohydrodynamics, (Lembege, B., Proc. 3rd International School for Space Simulation (1989), Cepadues-Editions: Cepadues-Editions Toulouse), 183 · Zbl 0726.76078 |
| [15] | Nishiguchi, A.; Yabe, T., J. Comput. Phys., 52, 390 (1983) · Zbl 0517.76016 |
| [16] | Eastwood, J. W., Comput. Phys. Commun., 48, 17 (1988) |
| [17] | B. J. A. Meltz, J. Comput. Phys., submitted.; B. J. A. Meltz, J. Comput. Phys., submitted. |
| [18] | Colella, P.; Woodward, P., J. Comput. Phys., 54, 115 (1984) · Zbl 0573.76057 |
| [19] | Moffatt, H. K., Magnetic Field Generation in Electrically Conducting Fluids (1978), Cambridge Univ. Press: Cambridge Univ. Press New York · Zbl 0393.76063 |
| [20] | Parker, R. L., (Proc. Roy. Soc. Ser. A, 291 (1966)), 60 |
| [21] | Chomaz, J. M., J. Fluid Mech., 187, 115 (1986) |
| [22] | Monaghan, J. J., J. Comput. Phys., 82, 1 (1989) · Zbl 0665.76124 |
| [23] | Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability (1961), Dover: Dover New York · Zbl 0142.44103 |
| [24] | A. L. Fogelson, Department of Mathematics, University of Utah, private communication.; A. L. Fogelson, Department of Mathematics, University of Utah, private communication. |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
