The Ohio State University
(Colloquium Tea held at 4:00 pm in 101A Crowley Hall)
Arbitrary Order Structure Preserving Discontinuous Galerkin Methods for Euler Equations with Gravitation
Hydrodynamical evolution in a gravitational field arises in many astrophysical and atmospheric problems. In this presentation, we will talk about arbitrary order structure preserving discontinuous Galerkin finite element methods for the Euler equations under gravitational fields, which can exactly capture the non-trivial steady state solutions, and at the same time maintain the non-negativity of some physical quantities. In addition, we consider the Euler–Poisson equations in spherical symmetry with an equilibrium state governed by the Lane–Emden equation, and design well-balanced and total-energy-conserving discontinuous Galerkin methods. Extensive numerical examples — including a toy model of stellar core-collapse with a phenomenological equation of state that results in core-bounce and shock formation — are provided to verify the well-balanced property, positivity-preserving property, high-order accuracy, total energy conservation and good resolution for both smooth and discontinuous solutions.