Oberseminar Mathematical Fluid Dynamics

We discuss structure-preserving numerical discretizations for the repulsive and attractive Euler-Poisson equations.
The scheme is fully discrete and structure preserving in the sense that it maintains a discrete energy law,
as well as hyperbolic invariant domain properties, such as positivity of the density and a minimum principle of
the specific entropy.
We discuss the underlying algebraic discretization technique based on collocation and convex limiting that
maintain hyperbolic invariants and a discrete energy law, and discuss recovery strategies to maintain the discrete
Gauss law. This is joint work with Fatemeh Nassajian Mojarrad, Jan S. Hesthaven and Philipp Öffner.