Adaptive Coupling of the Maximum-Entropy Cascade for the Vlasov Equation

Vlasov方程描述了基于粒子速度分布函数的等离子体流动。由于底层的高维相空间，包括空间和速度，其离散化仍然是一个计算挑战。最大熵方法是一种非线性闭合技术，它将分布函数的形状映射到相对较少的变量，由分布的矩给出。本计画研究最大熵近似在弗拉索夫方程中的应用。已经表明，暴力实现-直接实现最大熵，即使有少量的时刻-不产生一个有效的计划。相反，非线性分布和近似它的变量的数量必须选择性地只在计算域的关键部分。该项目将定义耦合条件和开关准则，并应用该方法模拟电子空穴行波。该项目是DFG研究单元“非均匀模型体耦合和界面耦合的结构保持数值方法（SNUBIC）"的一部分。

The Vlasov equation describes the flow of plasma based on the velocity distribution function of the particles. Due to the underlying high-dimensional phase space that includes space and velocity, its discretization remains a computational challenge. The maximum-entropy approach is a nonlinear closure technique that maps the shape of the distribtion function to a relatively low number of variables, given by the moments of the distribution. This project investigates the usage of the maximum-entropy approximation for the Vlasov equation. It has been shown that the brute-force implementation - directly implementing maximum-entropy even with a small number of moments - does not yield an efficient scheme. Instead the nonlinear distribution and the number of variables approximating it must be chosen selectively only in critical parts of the computational domain. The project will define coupling conditions and switching criteria, and apply the method to simulate electron hole travelling waves.This project is part of the DFG research unit "Structure-Preserving Numerical Methods for Bulk- and Interface-Coupling of Heterogeneous Models (SNuBIC)".