×

A finite volume formulation of the multi-moment advection scheme for Vlasov simulations of magnetized plasma. (English) Zbl 1348.35273

Summary: We present a finite volume version of the multi-moment advection scheme [the authors, J. Comput. Phys. 230, No. 17, 6800–6823 (2011; Zbl 1408.76595); J. Comput. Phys. 236, 81–95 (2013; Zbl 1286.78006)]. The scheme advances zeroth to second order piecewise moments at cell centers through their numerical fluxes obtained from one-dimensional high order interpolation. The modification simplifies the scheme without losing its high performance. We apply the scheme to two-dimensional electromagnetic Vlasov simulations of linear wave propagation and nonlinear magnetic reconnection problems. Our Vlasov simulation resolves microscopic structure of the non-Maxwellian plasma velocity distribution around the magnetic reconnection site as well as macroscopic structure of fluid quantities within the energy error of 2%, and is in good agreement with previous studies.

MSC:

35Q83 Vlasov equations
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
82D10 Statistical mechanics of plasmas
82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Birdsall, C. K.; Langdon, A. B., Plasma Physics via Computer Simulation (1991), Inst. of Phys. Publishing: Inst. of Phys. Publishing Bristol/Philadelphia
[2] Ghizzo, A.; Huot, F.; Bertrand, P., A non-periodic 2D semi-Lagrangian Vlasov code for laser-plasma interaction on parallel computer, J. Comput. Phys., 186, 47-69 (2003) · Zbl 1072.78524
[3] Cheng, C. Z.; Knorr, G., The integration of the Vlasov equation in configuration space, J. Comput. Phys., 22, 330-351 (1976)
[4] Nakamura, T.; Yabe, T., Cubic interpolated propagation scheme for solving the hyper-dimensional Vlasov-Poisson equation in phase space, Comput. Phys. Commun., 120, 122-154 (1999) · Zbl 1001.82003
[5] Filbet, F.; Sonnendrücker, E.; Bertrand, P., Conservative numerical schemes for the Vlasov equation, J. Comput. Phys., 172, 166-187 (2001) · Zbl 0998.65138
[6] Mangeney, A.; Califano, F.; Cavazzoni, C.; Travnicek, P., A numerical scheme for the integration of the Vlasov-Maxwell system of equations, J. Comput. Phys., 179, 495-538 (2002) · Zbl 1001.78025
[7] Schmitz, H.; Grauer, R., Comparison of time splitting and backsubstitution methods for integrating Vlasov’s equation with magnetic fields, Comput. Phys. Commun., 175, 86-92 (2006) · Zbl 1196.76058
[8] Umeda, T.; Togano, K.; Ogino, T., Two-dimensional full-electromagnetic Vlasov code with conservative scheme and its application to magnetic reconnection, Comput. Phys. Commun., 180, 365-374 (2009) · Zbl 1198.82060
[9] Sircombe, N. J.; Arber, T. D., VALIS: A split-conservative scheme for the relativistic 2D Vlasov-Maxwell system, J. Comput. Phys., 228, 4773-4788 (2009) · Zbl 1175.82059
[10] Crouseilles, N.; Respaud, T.; Sonnendrücker, E., A forward semi-Lagrangian method for the numerical solution of the Vlasov equation, Comput. Phys. Commun., 180, 1730-1745 (2009) · Zbl 1197.82012
[11] Minoshima, T.; Matsumoto, Y.; Amano, T., Multi-moment advection scheme for Vlasov simulations, J. Comput. Phys., 230, 6800-6823 (2011) · Zbl 1408.76595
[12] Minoshima, T.; Matsumoto, Y.; Amano, T., Multi-moment advection scheme in three dimension for Vlasov simulations of magnetized plasma, J. Comput. Phys., 236, 81-95 (2013) · Zbl 1286.78006
[14] Godfrey, B. B., Numerical Cherenkov instabilities in electromagnetic particle codes, J. Comput. Phys., 15, 504-521 (1974)
[15] Zenitani, S.; Hesse, M.; Klimas, A.; Black, C.; Kuznetsova, M., The inner structure of collisionless magnetic reconnection: The electron-frame dissipation measure and Hall fields, Phys. Plasmas, 18, 12, 122108 (2011)
[16] Schmitz, H.; Grauer, R., Kinetic Vlasov simulations of collisionless magnetic reconnection, Phys. Plasmas, 13, 9 (2006), 092309 · Zbl 1129.35473
[17] Terasawa, T., Hall current effect on tearing mode instability, Geophys. Res. Lett., 10, 475-478 (1983)
[18] Shay, M. A.; Drake, J. F.; Rogers, B. N.; Denton, R. E., Alfvénic collisionless magnetic reconnection and the Hall term, J. Geophys. Res., 106, 3759-3772 (2001)
[19] Pritchett, P. L., Geospace environment modeling magnetic reconnection challenge: Simulations with a full particle electromagnetic code, J. Geophys. Res., 106, 3783-3798 (2001)
[20] Hoshino, M.; Hiraide, K.; Mukai, T., Strong electron heating and non-Maxwellian behavior in magnetic reconnection, Earth, Planets, Space, 53, 627-634 (2001)
[21] Hoshino, M.; Mukai, T.; Terasawa, T.; Shinohara, I., Suprathermal electron acceleration in magnetic reconnection, J. Geophys. Res., 106, 25979-25998 (2001)
[22] Hesse, M.; Schindler, K.; Birn, J.; Kuznetsova, M., The diffusion region in collisionless magnetic reconnection, Phys. Plasmas, 6, 1781-1795 (1999)
[23] Kuznetsova, M. M.; Hesse, M.; Winske, D., Collisionless reconnection supported by nongyrotropic pressure effects in hybrid and particle simulations, J. Geophys. Res., 106, 3799-3810 (2001)
[24] Higashimori, K.; Hoshino, M., The relation between ion temperature anisotropy and formation of slow shocks in collisionless magnetic reconnection, J. Geophys. Res. (Space Phys.), 117, 1220 (2012)
[25] Petschek, H. E., Magnetic field annihilation, (Hess, W. N., The Physics of Solar Flares (1964)), 425
[26] Tsuneta, S., Structure and dynamics of magnetic reconnection in a solar flare, Astrophys. J., 456 (1996), 840
[27] Saito, Y.; Mukai, T.; Terasawa, T.; Nishida, A.; Machida, S.; Hirahara, M.; Maezawa, K.; Kokubun, S.; Yamamoto, T., Slow-mode shocks in the magnetotail, J. Geophys. Res., 100, 23567-23582 (1995)
[28] Evans, C. R.; Hawley, J. F., Simulation of magnetohydrodynamic flows — A constrained transport method, Astrophys. J., 332, 659-677 (1988)
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.