A discontinuous Galerkin method for the Vlasov-Poisson system
This work provides a new numerical method for simulating collisionless plasmas, which is important for plasma physics and fusion research, but the results are incremental as they benchmark against known problems without major performance breakthroughs.
The paper proposes a discontinuous Galerkin method for the Vlasov-Poisson system that is mass conservative and positivity-preserving for piecewise constant basis. Numerical tests show accurate results for linear Landau damping and nonlinear problems like two-stream instability, demonstrating the method's viability.
A discontinuous Galerkin method for approximating the Vlasov-Poisson system of equations describing the time evolution of a collisionless plasma is proposed. The method is mass conservative and, in the case that piecewise constant functions are used as a basis, the method preserves the positivity of the electron distribution function and weakly enforces continuity of the electric field through mesh interfaces and boundary conditions. The performance of the method is investigated by computing several examples and error estimates associated system's approximation are stated. In particular, computed results are benchmarked against established theoretical results for linear advection and the phenomenon of linear Landau damping for both the Maxwell and Lorentz distributions. Moreover, two nonlinear problems are considered: nonlinear Landau damping and a version of the two-stream instability are computed. For the latter, fine scale details of the resulting long-time BGK-like state are presented. Conservation laws are examined and various comparisons to theory are made. The results obtained demonstrate that the discontinuous Galerkin method is a viable option for integrating the Vlasov-Poisson system.