Numerical solution of plasma fluid equations using locally refined grids

This paper describes a numerical method for the solution of plasma fluid eq uations on block-structured, locally refined grids. The plasmas under consi deration are typical of those used for the processing of semiconductors. Th e governing equations consist of a drift-diffusion model of the electrons, together with an energy equation, coupled via Poisson's equation to a syste m of Euler equations for each ion species augmented with electric held, col lisional, and source/sink terms. A discretization previously developed for a uniform spatial grid is generalized to enable local grid refinement. This extension involves the time integration of the discrete system on a hierar chy of levels, each of which represents a degree of refinement, together wi th synchronization steps to ensure consistency across levels. This approach represents an advancement of methodologies developed for neutral flows usi ng block-structured adaptive mesh refinement (AMR) to include the significa nt additional effect of the electrostatic forces that couple the ion and el ectron fluid components. Numerical results that assess the accuracy and eff iciency of the method and illustrate the importance of using adequate resol ution are also presented.