AI 中文总结
针对弗拉索夫 - 泊松方程与道格拉斯 - 福克 - 普朗克碰撞算子耦合系统，构建基于局部宏观守恒的低秩间断伽辽金方法，利用数值低秩结构降低存储复杂度，经实验验证方法有效。
AI 中文摘要
本文构建了一种低秩、保结构的间断伽辽金（DG）方法来模拟与道格拉斯 - 福克 - 普朗克（DFP）碰撞算子耦合的弗拉索夫 - 泊松（VP）系统。在致密或弱碰撞等离子体中发生库仑碰撞时，电子会被推向低秩稳态。新的低秩格式利用这些数值低秩结构，极大降低VP - DFP系统模拟所需的存储复杂度。它是通过将库仑碰撞纳入系统，对先前建立的局部宏观守恒（LoMaC）方法的扩展。LoMaC性质确保离散水平上宏观质量、动量和能量的局部守恒。文中讨论了新方法细节并通过数值实验展示其有效性。
英文摘要
In this paper, we construct a low-rank, structure preserving discontinuous Galerkin (DG) method to simulate the Vlasov-Poisson (VP) system coupled with the Dougherty Fokker-Planck (DFP) collision operator. When Coulomb collisions occur in dense or weakly-collisional plasmas, electrons get pushed to a low-rank steady state. In many cases, the plasma arrives to this steady state quickly, meaning that for most of the run-time, the plasma consists mainly of numerical low-rank structures. Our new low-rank scheme is constructed to exploit these numerical low-rank structures to greatly reduce the needed storage complexity of simulations for the VP-DFP system. It is constructed as an extension of the previously established Local Macroscopic Conservative (LoMaC) method by incorporating Coulomb collisions into the system. The LoMaC property ensures local conservation of macroscopic mass, momentum, and energy at the discrete level. Details of the new method are discussed in this paper. Numerical experiments are performed to show the efficacy of the method.
Comments28 pages; 9 figures; planned publication in the Journal of Scientific Computing
