A conservative finite difference method for the numerical solution of plasma fluid equations

被引:38
作者
Colella, P
Dorr, MR
Wake, DD
机构
[1] Univ Calif Berkeley, Lawrence Berkeley Lab, Berkeley, CA 94720 USA
[2] Lawrence Livermore Natl Lab, Livermore, CA 94551 USA
关键词
models; numerical methods; finite difference methods; ionized gas flow in electromagnetic fields; plasmic flow;
D O I
10.1006/jcph.1998.6136
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
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 internal 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 advancement 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 propagation 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.
引用
收藏
页码:168 / 193
页数:26
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