An Active Flux Method for the Vlasov-Maxwell System

我们开发了一种用于无碰撞等离子体的Vlasov/Maxwell系统的有源通量方法。有源通量法是有限体积法的一种新形式，它既使用单元平均值，也使用物理量的点值作为自由度。由于底层的Vlasov方程具有六维平流方程的结构，且点值的运动特性易于计算，因此有源通量法非常适合求解Vlasov方程。有源通量法具有高阶精度和空间、时间上的紧凑特点。附加自由度，即点值，将用于构造满足附加约束（如能量守恒）的方案。为了将该方法应用于相关的高维物理问题，高性能计算方面也将发挥重要作用。该项目是DFG研究单元“异构模型体和接口耦合的结构保持数值方法（SNuBIC）”的一部分。

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)".