Verification of 2D × 2D and Two-Species Vlasov-Poisson Solvers,

Abstract

In [2], 1D×1D two-species Vlasov-Poisson simulations are performed by the semi-Lagrangian method. Thanks to a classical first order dispersion analysis, we are able to check the validity of their simulations; the extension to second order is performed and shown to be relevant for explaining further details. In order to validate multi-dimensional effects, we propose a 2D × 2D single species test problem that has true 2D effects coming from the sole second order dispersion analysis. Finally, we perform, in the same code, full 2D × 2D non linear two-species simulations with mass ratio 0:01, and consider the mixing of semi-Lagrangian and Particle-in-Cell methods.

Semi-Lagrangian Vlasov simulation on GPUs

“…The time evolution of the electric field and some snapshots of the density function are shown in Figure 13. We remark that these results agree well with what has been reported in the literature (see, for example, [22,3]). Figure 13 shows both single and double precision results, which are almost indistinguishable in the plots.…”

Long-time behavior of second order linearized Vlasov-Poisson equations near a homogeneous equilibrium

“…We recall that these poles drive the asymptotic behavior of µ(k) through formula (7). The frequencies (I) and (II) have already been identified in our preliminary work on this subject [4], but not the frequency (III). We emphasize that all the three type of frequencies are listed in [13], which makes our analysis coherent with the physics litterature.…”

“…Remark 7. It is quite direct to extend the classical linear analysis of the Vlasov Poisson with 1 specie to the case of multi-species charged particles (see § 3.1.2 in [4]). Similarly, we expect that it would be possible to extend our second order analysis to the multi-species case.…”

“…Similarly, we expect that it would be possible to extend our second order analysis to the multi-species case. Actually, such an extension is discussed in our preliminary work ( § 5.1 in [4]) to explain more precisely the numerical results associated with a multi-species test case introduced in [2].…”

A performance comparison of semi-Lagrangian discontinuous Galerkin and spline based Vlasov solvers in four dimensions

“…Thus, by using the splitting approach outlined above we have reduced the task of computing a numerical approximation to the four-dimensional Vlasov--Poisson equation to computing two-dimensional translations in phase space. However, this can be further simplified by splitting equation (2) into an advection in the…”