Numerical solution of plasma fluid equations using locally refined grids

This paper describes a numerical method for the solution of plasma fluid equations on block-structured, locally refined grids. The plasmas under consideration are typical of those used for the processing of semiconductors. The governing equations consist of a drift-diffusion model of the electrons, together with an energy equation, coupled via Poisson's equation to a system of Euler equations for each ion species augmented with electric field, collisional, 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 hierarchy of levels, each of which represents a degree of refinement, together with synchronization steps to ensure consistency across levels. This approach represents an advancement of methodologies developed for neutral flows using block-structured adaptive mesh refinement (AMR) to include the significant additional effect of the electrostatic forces that couple the ion and electron fluid components. Numerical results that assess the accuracy and efficiency of the method and illustrate the importance of using adequate resolution are also presented.