2024/02/06 by Zhixin Lu, Meng Guo, Lu, Zhixin +5
Engineering · Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Gamma-ray bursts and supernovae #Mathematical Physics (math-ph) #Particle Dynamics in Fluid Flows #Plasma Physics (physics.plasm-ph) #Solar and Space Plasma Dynamics
paper · pdf · doi:10.48550/arxiv.2402.03856
openalex publication_date 2024/02/06 · openalex created_date 2024/02/08 · openalex updated_date 2026/07/28
In this study, we consider a numerical implementation of the nonlinear Rosenbluth-Trubnikov collision operator for particle simulations in plasma physics in the framework of the finite element method (FEM). The relevant particle evolution equations are formulated as stochastic differential equations, both in the Stratonovich and Itô forms, and are then solved with advanced high-order stochastic numerical schemes. Due to its formulation as a stochastic differential equation, both the drift and diffusion components of the collision operator are treated on an equal footing. Our investigation focuses on assessing the accuracy of these schemes. Previous studies on this subject have used the Euler-Maruyama scheme, which, although popular, is of low order, and requires small time steps to achieve satisfactory accuracy. In this work, we compare the performance of the Euler-Maruyama method to other high-order stochastic methods known in the stochastic differential equations literature. Our study reveals advantageous features of these high-order schemes, such as better accuracy and improved conservation properties of the numerical solution. The main test case used in the numerical experiments is the thermalization of isotropic and anisotropic particle distributions.