Lagrangian/Eulerian solvers and simulations for Vlasov-Poisson

• Main Authors: Guisset Sebastien, Gutnic Michael, Helluy Philippe, Massaro Michel, Navoret Laurent, Pham Nhung, Roberts Malcolm
• Format: Article
• Language: English
• Published: EDP Sciences 2016-03-01
• Series: ESAIM: Proceedings and Surveys
• Online Access: http://dx.doi.org/10.1051/proc/201653008

We construct a hyperbolic approximation of the Vlasov equation using a method of reduction [10, 14, 22] in which the dependency on the velocity variable is removed. The reduction relies on a semi-discrete finite element approximation in the velocity variable. We apply Gauss-Lobatto numerical integration in velocity space, reducing the hyperbolic system to a system of transport equations for which the transport velocities are the Gauss-Lobatto points. The transport equations are coupled through a zero-order term that represents the electromagnetic forces. We solve the resulting system by a splitting approach: the homogeneous transport equations are solved by a split semi-Lagrangian method and the source term is applied independently. We also present preliminary comparisons with another transport solver based on the discontinuous Galerkin method.