A finite element code for the simulation of one-dimensional Vlasov plasmas I. Theory
Journal of Computational Physics
A finite element code for the simulation of one-dimensional Vlasov plasmas. II.Applications
Journal of Computational Physics
Computer simulation using particles
Computer simulation using particles
Journal of Computational Physics
A splitting algorithm for Vlasov simulation with filamentation filtration
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Numerical study on Landau damping
Physica D
Conservative numerical schemes for the Vlasov equation
Journal of Computational Physics
Outflow Boundary Conditions for the Fourier Transformed One-Dimensional Vlasov–Poisson System
Journal of Scientific Computing
Plasma Physics Via Computer
SIAM Journal on Numerical Analysis
A numerical scheme for the integration of the Vlasov--Maxwell system of equations
Journal of Computational Physics
Symmetric and Nonsymmetric Discontinuous Galerkin Methods for Reactive Transport in Porous Media
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Journal of Computational Physics
On maximum-principle-satisfying high order schemes for scalar conservation laws
Journal of Computational Physics
Hybrid semi-Lagrangian finite element-finite difference methods for the Vlasov equation
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
Energy-conserving discontinuous Galerkin methods for the Vlasov-Ampère system
Journal of Computational Physics
Hi-index | 31.47 |
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 of the 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.