Communications on Applied Mathematics and Computation, 2022, 4(1): 34-59
Conservative Discontinuous Galerkin/Hermite Spectral Method for the Vlasov-Poisson System
Francis Filbet1, Tao Xiong2
1. Institut de Mathématiques de Toulouse, Université Paul Sabatier, Toulouse 31062, France;
2. School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University, Xiamen 361005, Fujian Province, China
Abstract: We propose a class of conservative discontinuous Galerkin methods for the Vlasov-Poisson system written as a hyperbolic system using Hermite polynomials in the velocity variable. These schemes are designed to be systematically as accurate as one wants with provable conservation of mass and possibly total energy. Such properties in general are hard to achieve within other numerical method frameworks for simulating the Vlasov-Poisson system. The proposed scheme employs the discontinuous Galerkin discretization for both the Vlasov and the Poisson equations, resulting in a consistent description of the distribution function and the electric field. Numerical simulations are performed to verify the order of the accuracy and conservation properties.
Key words: Energy conserving, Discontinuous Galerkin method, Hermite spectral method, Vlasov-Poisson
https://link.springer.com/article/10.1007/s42967-020-00089-z