Past Event: Oden Institute Seminar

Goal-Adaptive Moment Hierarchies for the Boltzmann equation

Michael Abdelmalik , ICES, University of Texas at Austin

Abstract

In this presentation we consider a numerical approximation technique for the Boltzmann equation based on a moment-system approximation in velocity dependence and a discontinuous Galerkin (DG) finite-element approximation in position dependence. The closure relation for the moment systems derives from the minimization of a suitable divergence. This divergence-based closure yields a hierarchy of tractable symmetric hyperbolic moment systems that retain the fundamental structural properties of the Boltzmann equation. The resulting combined DG moment method corresponds to a Galerkin approximation of the Boltzmann equation in re-normalized form. The new moment-closure formulation engenders a new upwind numerical flux function that ensures entropy stability of the DG finite-element approximation. The Galerkin form of moment methods enables the estimation of a posteriori errors, while the hierarchical structure provides an intrinsic mode for local model refinement. We will present numerical results for the DG finite element moment method and the goal-oriented adaptive refinement.