A forward semi-Lagrangian method for the numerical solution of the Vlasov equation

This work deals with the numerical solution of the Vlasov equation, which provides a kinetic description of the evolution of a plasma, and is coupled with Poisson's equation. A new forward semi-Lagrangian method is developed. The distribution function is updated on a Eulerian grid, and the pseudo-particles located on the mesh nodes follow the characteristics of the equation forward for one time step, and are deposited on the 16 nearest nodes. This is an explicit way of solving the Vlasov equation on a grid of the phase space, which makes it easier to develop high-order time schemes than the backward method.