### Project B4

**Principal Investigator:**

*Manuel Torrilhon, Applied and Computational Mathematics, RWTH Aachen*

**Main Collaborators in the Research Unit:**

*Christiane Helzel, Applied Mathematics, Heinrich-Heine-University*

*Rainer Grauer, Theoretical Physics I, Ruhr-University Bochum*

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

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 reamins 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.

Complex Fluids
(C) Coupling Algorithms