Past Event: Oden Institute Seminar

Aspects of Discontinuous Galerkin Schemes for Fluid and Kinetic Simulations of Plasmas

Ammar Hakim, Princeton Plasma Physics Laboratory

Abstract

A large class of kinetic and fluid problems in plasma physics can be expressed using a Hamiltonian approach. Such systems consist of an advection equation coupled to field equations. The advection speeds are determined from the Hamiltonian and a Poisson bracket, and, in many instances, the fields are computed using elliptic equations. One feature of such systems are the existence of quadratic invariants, like energy and, in context of incompressible fluid flow, enstrophy. In this talk we present extensions of discontinuous Galerkin algorithms to solve such equations. We show that with a proper choice of basis functions for the advection and elliptic equations the DG schemes can conserve energy exactly. Further, with a choice of central fluxes the enstrophy (the L2 norm of the solution) can also be conserved exactly. Extension to the scheme to handle discontinuous Hamiltonians are developed. Application of these schemes to incompressible flow problems, drift wave turbulence and Vlasov-Poisson equations are presented.