Journal of Computational Physics 149, 168–193 (1999) Article ID jcph.1998.6136, available online at http://www.idealibrary.com on A Conservative Finite Difference Method for the Numerical Solution of Plasma Fluid Equations 1 Phillip Colella, ∗ Milo R. Dorr,† and Daniel D. Wake† ∗ Lawrence Berkeley National Laboratory, One Cyclotron Road, MS 50D, Berkeley, California 94720; †Lawrence Livermore National Laboratory, P.O. Box 808, L-561, Livermore, California 94551 E-mail: MiloDorr@llnl.gov Received April 14, 1998; revised October 9, 1998 This paper describes a numerical method for the solution of a system of plasma fluid equations. The fluid model is similar to those employed in the simulation of high-density, low-pressure plasmas used in semiconductor processing. The governing equations consist of a drift-diffusion model of the electrons, together with an inter- nal energy equation, coupled via Poisson’s equation to a system of Euler equations for each ion species augmented with electrostatic force, collisional, and source/sink terms. The time integration of the full system is performed using an operator splitting that conserves space charge and avoids dielectric relaxation timestep restrictions. The integration of the individual ion species and electrons within the time-split advance- ment is achieved using a second-order Godunov discretization of the hyperbolic terms, modified to account for the significant role of the electric field in the prop- agation of acoustic waves, combined with a backward Euler discretization of the parabolic terms. Discrete boundary conditions are employed to accommodate the plasma sheath boundary layer on underresolved grids. The algorithm is described for the case of a single Cartesian grid as the first step toward an implementation on a locally refined grid hierarchy in which the method presented here may be applied on each refinement level. c  1999 Academic Press Key Words: models; numerical methods; finite difference methods; ionized gas flow in electromagnetic fields; plasmic flow. 1. INTRODUCTION Many plasma phenomena can be predicted using mathematical models in which the plasma is treated as a fluid comprised of charged species. One example is provided by 1 This work was supported by the Applied Mathematical Sciences Program of the Office of Mathematics, Information and Computational Sciences, of the U.S. Department of Energy under Contract DE-AC03-76SF00098 with Lawrence Berkeley National Laboratory and by Lawrence Livermore National Laboratory under Contract W-7405-Eng-48. 168 0021-9991/99 $30.00 Copyright c  1999 by Academic Press All rights of reproduction in any form reserved.