Discontinuous Galerkin discretization of conservative dynamical low-rank approximation schemes for the Vlasov–Poisson equation

Abstract A numerical dynamical low-rank approximation (DLRA) scheme for the solution of the Vlasov–Poisson equation is presented. Based on the formulation of the DLRA equations as Friedrichs’ systems in a continuous setting, it combines recently proposed conservative DLRA methods with a discontinuous Galerkin discretization. The resulting scheme is shown to ensure mass and momentum conservation at the discrete level. In addition, a new formulation of the conservative integrator is proposed based on its interpretation as a tangent space projector splitting scheme. Numerical experiments validate our approach in one- and two-dimensional simulations of Landau damping. As a demonstration of feasibility, it is also shown that the rank-adaptive unconventional integrator can be combined with mesh adaptivity.