Young Researchers Workshop:
Multiscale phenomena: modeling, analysis and computation

A Discontinuous Galerkin implementation of the entropy-based moment closure for linear kinetic equations

Graham Alldredge

RWTH Aachen University


Entropy-based moment closures for kinetic equations have particularly attractive theoretical properties, including hyperbolicity, positivity, and entropy dissipation, but there remain many obstacles to a practical implementation, particularly one which is high-order. A primary obstacle is that although the method is only defined for realizable moments (those consistent with a positive distribution), nonrealizable moments arise due to numerical errors, We have implemented a third-order solver, using the Runge-Kutta discontinuous Galerkin method, with a limiter which takes nonrealizable moments back into the realizable set. Instead of the exact realizable set, whose description is intractably complex, we use the realizable set generated when the defining integrals are approximated by quadrature. This set is a convex polytope, and using its half-space representation we are able to compute the intersection of the polytope with lines between realizable and nonrealizable moments. We present numerical results including a convergence test and benchmark problems.