Tests of Limiters for Discontinuous Galerkin Advection Algorithms

In continuum kinetic plasma simulations, maintenance of the positivity of the distribution function and monotonicity (avoiding numerically generated oscillations) is important for a physical solution. Here, we investigate issues surrounding maintaining positivity (and the more restrictive property of monotonicity) when using a discontinuous Galerkin (DG) approach. We are particularly interested in methods that do not break conservation properties of the solution algorithm and are amenable to implementation in high-dimensional spaces without prohibitive computational difficulty. While finite volume approaches keep track of a cell mean, the discontinuous Galerkin method makes use of a number of higher solution moments and interpolations to quadrature points using these moments. Because of this fact, positivity-enforcing methods that are successful for finite volume means do not necessarily guarantee a positive discontinuous Galerkin solution. Performance of several different limiting schemes on some tests cases will be shown.