7 research outputs found
A combined discontinuous Galerkin and finite volume scheme for multi-dimensional VPFP system
We construct a numerical scheme for the multi-dimensional Vlasov-Poisson-Fokker-Planck system based on a combined finite volume (FV) method for the Poisson equation in spatial domain and the streamline diffusion (SD) and discontinuous Galerkin (DG) finite element in time, phase-space variables for the Vlasov-Fokker-Planck equation
High order and energy preserving discontinuous Galerkin methods for the Vlasov-Poisson system
We present a computational study for a family of discontinuous Galerkin
methods for the one dimensional Vlasov-Poisson system that has been recently
introduced. We introduce a slight modification of the methods to allow for
feasible computations while preserving the properties of the original methods.
We study numerically the verification of the theoretical and convergence
analysis, discussing also the conservation properties of the schemes. The
methods are validated through their application to some of the benchmarks in
the simulation of plasma physics.Comment: 44 pages, 28 figure
A Convergent Finite Volume Method for a Kinetic Model for Interacting Species
We propose an upwind finite volume method for a system of two kinetic
equations in one dimension that are coupled through nonlocal interaction terms.
These cross-interaction systems were recently obtained as the mean-field limit
of a second-order system of ordinary differential equations for two interacting
species. Models of this kind are encountered in a myriad of contexts, for
instance, to describe large systems of indistinguishable agents such as cell
colonies, flocks of birds, schools of fish, herds of sheep. The finite volume
method we propose is constructed to conserve mass and preserve positivity.
Moreover, convex functionals of the discrete solution are controlled, which we
use to show the convergence of the scheme. Finally, we investigate the scheme
numerically
Numerical Scheme for the One-Dimensional Vlasov-Poisson Equation Using Bi-Orthogonal Spline Wavelets
In this paper, a numerical scheme for solving the Vlasov-Poisson equations is proposed. It is based on bi-orthogonal compactly supported spline wavelets. The interest of these wavelets used in this method is their precision in computations. For solving the Vlasov equation, a Strang splitting in time and a semi-lagrangian method are used. For the Poisson equation, a solver based only on wavelets is presented
Discontinuous Galerkin methods for the one-dimensional Vlasov-Poisson system
We construct a new family of semi-discrete numerical schemes for the approximation of the one-dimensional periodic Vlasov-Poisson system. The methods are based on the coupling of discontinuous Galerkin approximation to the Vlasov equation and several finite element (conforming, non-conforming and mixed) approximations for the Poisson problem. We show optimal error estimates for the all proposed methods in the case of smooth compactly supported initial data. The issue of energy conservation is also analyzed for some of the methods