A multiscale hybrid Monte-Carlo-Gaussian Coulomb-Collision Algorithm for Hybrid Kinetic-Fluid Simulations

Coulomb collisions in particle simulations for weakly coupled plasmas are typically modeled by Monte-Carlo (MC) methods [1]. One of the main disadvantages of MC is the timestep accuracy constraint γ△t<<1 to resolve the collision frequency γ [2]. The constraint becomes extremely stringent for self-collisions in the presence of high-Z species, and for interspecies collisions with large mass disparities, rendering such simulations impractical. To overcome these difficulties, we explore a hybrid MC-Gaussian model for hybrid kinetic-fluid simulations. Specifically, we devise a collisional algorithm that leverages Maxwellians (i.e. isotropic Gaussians) [3] for both highly collisional kinetic species and fluid ones. We perform Gaussian-particle collisions using the Lemons method [4], which we have improved by more careful treatment of low-relative-speed particles. We extend the standard MC method [1] for particle-particle collisions with a new variable-particle-weight-pairing scheme without losing conservation properties. The new hybrid MC-Gaussian method is strictly conservative and is orders of magnitude faster than straight MC. We will illustrate the accuracy and performance of the proposed method with several examples of varying complexity, including relaxation of species with disparate charges and masses, and transport problems with kinetic-ion-fluid-electron hybrid simulations.

[1] Takizuka, T., Abe, H. Journal of computational physics, (1977) 25: 205-219.

[2] Dimits, A. M., Wang, C., Caflisch, R., Cohen, B. I., & Huang, Y. Journalof Computational Physics (2009) 228: 4881-4892.

[3] Lemons, D.S., Winske, D., Daughton, W. and Albright, B., Journal ofComputational Physics, (2009) 228(5), pp.1391-1403.

[4] Echim MM, Lemaire J, & Lie-Svendsen Ø. Surveys in geophysics (2011) 32:1-70.