### Project B5

**Principal Investigator:**

*Katharina Kormann, Research Group Numerics, Ruhr-Universität Bochum*

**Main Collaborators in the Research Unit:**

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

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

## Dynamical Low-Rank Approximation Methods for Two-Particle Kinetic Equations

Two-particle kinetic differential equations provide a comprehensive description of plasmas by taking two-particle interations into account.
However, incorporating the second particle into the model doubles the number of degrees of freedom in the system, so that computational storage of the necessary data for all but the smallest and simplest of systems is not possible, which in turn places a severe bottleneck on the system sizes that can be studied. The aim of this project is to raise this computational storage bottleneck by reducing the severely high dimensionality of two-particle kinetic systems and to develop, implement, and analyze a first numerical simulation tool for the two-particle kinetic equation. We will consider a representation that couples a kinetic description of the one-particle distribution function with the two-particle correlation function and a field equation describing the (electric) field induced by the particles. The numerical solution strategy will focus on an efficient low-rank splitting and a structure-preserving spatial discretization.

Moment Models
(C) Coupling Algorithms