Spectral velocity discretizations for the Vlasov-Maxwell equations

Abstract

Abstract Two Hermite based spectral methods are examined. A method based on an asymmetric expansion in Hermite polynomials offers theoretical advantages over other spectral basis sets for the treatment of the velocity variables in the Vlasov-Maxwell equations of plasma kinetic theory. It provides for exact conservation of energy, momentum, and particles (in a fully discrete system, not just as the discretization is refined), and this conservation is not effected by the use of velocity space filters during time-stepping. The asymmetric Hermite method exactly solves the spatially uniform problem (plasma oscillations), and both Hermite based methods exactly recover the temporal behavior of retained moments for free streaming in a periodic system. Yet the cost of these Hermite methods scales only linearly with the number of degrees for freedom, just like a finite difference method, and in fact the number of runtime operations required per degree of freedom in the asymmetric method can be essentially identical...