Direct simulation Monte Carlo schemes for Coulomb interactions in plasmas

Résumé

We consider the development of Monte Carlo schemes for molecules with Coulomb interactions. We generalize the classic algorithms of Bird and Nanbu-Babovsky for rarefied gas dynamics to the Coulomb case thanks to the approximation introduced by Bobylev and Nanbu [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, Physical Review E, vol. 61, no. 4, pp. 4576–4586, 2000.]. Thus, instead of considering the original Boltzmann collision operator, the schemes are constructed through the use of an approximated Boltzmann operator. With the above choice larger time steps are possible in simulations; moreover the expensive acceptance-rejection procedure for collisions is avoided and every particle collides. Error analysis and comparisons with the original Bobylev-Nanbu (BN) scheme are performed. The numerical results show agreement with the theoretical convergence rate of the approximated Boltzmann operator and the better performance of Bird-type schemes with respect to the original scheme.