An Active Flux Method for the Vlasov-Maxwell System

本文对无碰撞等离子体中的Vlasov/麦克斯韦系统发展了一种新的有限体积方法--主动通量法，它以物理量的单元平均值和点值作为自由度。由于Vlasov方程具有六维平流方程的结构，并且可以容易地计算点值的运动特性，因此主动通量方法非常适合于Vlasov方程。主动通量方法具有高阶精度，并且在空间和时间上具有紧凑的模板。该方法利用附加自由度即点值构造出满足能量守恒等附加约束的格式，为了将该方法应用于相应的高维物理问题，高性能计算方面也将发挥重要作用。该项目是DFG研究单位“体和界面的结构保持数值方法”的一部分，异构模型耦合（SNUBIC）。

We develop an Active Flux method for the Vlasov/Maxwell system for a collisionless plasma.The Active Flux method is a new form of a finite volume method which uses both cell average values as well as point values of the physical quantities as degrees of freedom. Since the underlying Vlasov equation has the structure of a six dimensional advection equation and the characteristics for the motion of the point values can be easily calculated, the Active Flux method is ideally suited for the Vlasov equation. Active Flux methods are high order accurate and have a compact stencil in space and time. The additional degrees of freedom, i.e. the point values, will be used to construct schemes which satisfy additional constraints such as conservation of energy.In order to apply the method to relevant high dimensional physical problems, aspects of high performance computing will also play an important role.This project is part of the DFG research unit "Structure-Preserving Numerical Methods for Bulk- and Interface-Coupling of Heterogeneous Models (SNuBIC)".