Simplex-in-Cell Technique for Collisionless Plasma Simulations

摘要

We extend the simplex-in-cell (SIC) technique recently introduced in thecontext of collisionless dark matter fluids (Abel et al. 2012; Hahn et al.2012) to the case of collisionless plasmas. The six-dimensional phase spacedistribution function $f(\mathbf x,\mathbf v)$ is represented by an ensemble ofthree-dimensional manifolds, which we refer to as sheets. The electricpotential field is obtained by solving the Poisson equation on a uniform mesh,where the charge density is evaluated by a spatial projection of the phasespace sheets. The SIC representation of phase space density facilitates robust,high accuracy numerical evolution of the Vlasov-Poisson system usingsignificantly fewer tracer particles than comparable particle-in-cell (PIC)approaches by reducing the numerical shot-noise associated with the latter. Weintroduce the SIC formulation and describe its implementation in a new code,which we validate using standard test problems including plasma oscillations,Landau damping, and two stream instabilities in one dimension. Merits of thenew scheme are shown to include higher accuracy and faster convergence rates inthe number of particles. We finally motivate and outline the efficientapplication of SIC to higher dimensional problems.