论文标题
各向同性多物种Rosenbluth- fokker- planck方程
A mass-energy-conserving discontinuous Galerkin scheme for the isotropic multispecies Rosenbluth--Fokker--Planck equation
论文作者
论文摘要
Rosenbluth-Fokker-Planck方程的结构保留离散化仍然是一个开放的问题，尤其是对于粒子碰撞而言。在本文中，引入了一种质量能量的各向同性Rosenbluth-Fokker-Planck方案。与节能相关的结构是数学意义上的偏斜对称性，而在物理意义上的作用反应定律。通过在能量矩方程的体积积分上使用逐个组成来获得热弛豫项，因此选择了不连续的Galerkin方法来保留偏斜的对称性。不连续的Galerkin方法使人们能够在不违反保护定律的情况下引入非线性朝外通量。一些实验表明，保守方案仅在圆形误差中维持质量能的保存，并且仅在其正式准确性的截断误差中再现分析平衡。
Structure-preserving discretization of the Rosenbluth-Fokker-Planck equation is still an open question especially for unlike-particle collision. In this paper, a mass-energy-conserving isotropic Rosenbluth-Fokker-Planck scheme is introduced. The structure related to the energy conservation is skew-symmetry in mathematical sense, and the action-reaction law in physical sense. A thermal relaxation term is obtained by using integration-by-parts on a volume integral of the energy moment equation, so the discontinuous Galerkin method is selected to preserve the skew-symmetry. The discontinuous Galerkin method enables ones to introduce the nonlinear upwind flux without violating the conservation laws. Some experiments show that the conservative scheme maintains the mass-energy-conservation only with round-off errors, and analytic equilibria are reproduced only with truncation errors of its formal accuracy.
