On discontinuous Galerkin approximations of Boltzmann moment systems with Levermore closure

This work considers the discontinuous Galerkin (DG) finite element discretization of first-order systems of conservation laws derivable as moments of the kinetic Boltzmann equation with Levermore [C.D. Levermore, Moment closure hierarchies for kinetic theories, J. Statist. Phys. 83 (5–6) (1996) 1021–1065] closure. Using standard energy analysis techniques, a new class of energy stable numerical flux functions are devised for the DG discretization of Boltzmann moment systems. Simplified energy stable numerical fluxes are then constructed which replace exact state space integration in the numerical flux with Gauss–Lobatto quadrature. Numerical results for supersonic flow over a cylinder geometry in the continuum and transitional regimes using 5 and 10 moment approximations are presented using the newly devised DG discretizations.