Front tracking scheme for direct kinetic simulations

Summary form only given. Direct kinetic (DK) simulations solve kinetic equations such as the Vlasov equation on discretized phase space to obtain distribution functions directly. In comparison to conventional particle simulations, the statistical noise due to the use of macro-particles is eliminated. [1] Although smooth distribution functions can be obtained using a DK simulation, numerical error is generated when solving the hyperbolic partial differential equation and propagates in the velocity space, which results in artificial heating of particles. In particular, it is difficult to capture the transport of a low temperature gas or plasma since the velocity distribution resembles a delta function or a discontinuity with a given number of cells. Although numerical error can be reduced by increasing the number of grid points or by using high order numerical schemes, numerical error will always occur and propagate. In this study, we propose a new method that tracks the maximum and minimum velocities which one particle can achieve in the physical coordinate, called the “front.” Transport of particles and propagation of the numerical error are limited beyond the front. While computational cost is on the same order, solutions obtained using the front tracking scheme are more accurate than those calculated without the scheme. The numerical method is tested in a collisionless sheath problem with and without emitted electrons from the wall as well as in the transient plasma of a Hall thruster.