Past Event: Oden Institute Seminar

Discrete Simulation Monte Carlo (DSMC) methods for simulations of Coulomb collisions in multi-component plasma

A.V. Bobylev*, S.A. Karpov** and I.F.Potapenko**, *Department of Mathematics, Karlstad University, Sweden **Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow

Abstract

The general DSMC method for solving Boltzmann equation for long-range potentials and Landau-Fokker-Planck equation was proposed by Bobylev and Nanbu in 2000 [1] (partly as a development of earlier approach of Nanbu [2] to Coulomb collisions). The methods of [1,2] were later applied to various model problems of plasma physics, discussed in detail and further developed by several authors (see, for example, [3,4] and references in [4]). However, the general method of [1] was not clearly understood and therefore many authors still use a more complicated original scheme of [2] with reference to [1] just for the formal proof of consistency with the Landau-Fokker-Planck equation. The reason is that the first presentation of the method was done in [1] in too formal and general way. We present in this paper a completely different approach, which leads to basically the same general method, but makes its essence absolutely clear and transparent. The method is explained for the general case of multi-component plasma. We also present some rigorous estimates for accuracy of the method. Finally some numerical results on typical problems of physics of collisional plasma are presented and discussed. References: 1. A.V.Bobylev and K.Nanbu, Theory of collision algorithms for gases and plasmas based on the Boltzmann equation and the Landau-Fokker-Planck equation, Phys.Rev.E 61, 4576-4586 (2000). 2. K.Nanbu, Theory of cumulative small-angle collisions in plasmas, Phys.Rev. E 55, 4642-4652 (1997). 3. A.V.Bobylev, E.Mossberg and I.F.Potapenko, A DSMC method for the Landau-Fokker-Planck equation, in the book Rarefied Gas Dynamics (Proc. of 25th RGD Symposium, St. Petersburg, July 2006), Eds. M.S.Ivanov and A.K.Rebrov, 479-483, Novosibirsk 2007. 4. G.Dimarco, R.Caflisch, L.Pareschi, Direct Simulation Monte Carlo schemes for Coulomb interactions in plasmas, Commun. Appl. Indust. Math. 1, 72-91 (2010).