### Project B1

**Principal Investigator:**

*Gregor Gassner, Department of Mathematics and Computer Science,
University of Cologne*

**Main Collaborators in the Research Unit:**

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

*Stefanie Braun, Applied and Computational Mathematics, RWTH Aachen
University*

*Eric Sonnendrücker, Institute for Plasma Physics Max-Planck/TU Munich*

## A Hybrid Entropy-Dissipative Spectral Element Method for Magnetized Plasmas

The research goal of this project is to construct a hybrid spectral element method for the two-fluid plasma system. The non-linear fluid part for ions and electrons is discretized with split-form discontinuous Galerkin methods that satisfy a summation-by-parts property, while the Maxwell system is discretized with mimetic spectral elements. Split-form discontinuous Galerkin methods allow to mimic the entropic behavior of the system by constructing discrete versions of non-linear chain-rules. Mimetic spectral elements are constructed such, that the divergence constraints on the electric and magnetic fields are exactly satisfied. Both methods rely on tensor product basis functions that originate from 1D Lagrange interpolation on Legendre-Gauss-Lobatto nodes. A special focus is on the coupling of these two structure preserving methodologies to obtain a hybrid, stable and high-order accurate spectral element scheme for the two-fluid plasma system that is consistent to the thermodynamic entropy, locally conservative for mass, momentum and energy, and that exactly preserves the divergence constraints on electric and magnetic fields.

(B) Numerical Methods for Coupling
Kinetic Simulations