Numerical integration of the Vlasov equation

Convergence of a semi-Lagrangian scheme for the reduced Vlasov–Maxwell system for laser–plasma interaction

“…Even if this kind of method enables to get some satisfactory results with relatively few particles, for some applications however, it is well known that the numerical noise becomes too important. Consequently, methods relying on a discretization of the phase space have been proposed (see [18,17]) and seem to be very efficient when the particles in the tail of the distribution play an important role for example. Among these methods, finite volume schemes (see [5,9,12,13]) have been successfully implemented; even if they are known to be robust, they are quite dissipative and suffer from the fact that they are constrained by a severe CFL condition on the time step.…”

Comparison of Vlasov solvers for spacecraft charging simulation

“…Moreover the computational time required seems to be very long. -Another approach consists in discretizing the phase space, and interpreting the Vlasov equation as a conservation law in phase space, to propose a Finite Volume approximation (or flux balance method) [12,15,16,28]. -Finally semi-Lagrangian methods combine space phase discretization and integration along characteristics, through an interpolation step which is intended to project as smartly as possible the endpoint of the path on the grid after a time step.…”

Hermite Spline Interpolation on Patches for Parallelly Solving the Vlasov-Poisson Equation

“…Even though these methods produce satisfactory results with relatively few particles, for some applications (in particular, when particles in the tail of the distribution function play an important physical role, or when one wants to study the influence of density fluctuations which are at the origin of instabilities), it is well known that the numerical noise inherent in the particle methods becomes too significant. Consequently, methods which discretize the Vlasov equation on a phase space grid have been proposed (see (Feix et al, 1994;Filbet et al, 2001;Filbet and Sonnendrücker, 2003;Ghizzo et al, 1996;Ghizzo et al, 1990;Shoucri and Knorr, 1974; for plasma physics and (Bermejo, 1991;Staniforth and Coté, 1991) for other applications). Among these Eulerian methods, the semi-Lagrangian method consists in computing directly the distribution function on a Cartesian grid of the phase space.…”