Numerical solution of plasma fluid equations using locally refined grids.

*(English)*Zbl 0954.76062Summary: 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 to include the significant additional effect of the electrostatic forces that couple the ion and electron fluid components. Numerical results assess the accuracy of the method and illustrate the importance of using adequate resolution.

##### MSC:

76M20 | Finite difference methods applied to problems in fluid mechanics |

76X05 | Ionized gas flow in electromagnetic fields; plasmic flow |

82D37 | Statistical mechanics of semiconductors |

##### Keywords:

Euler equations for ion species; effect of electrostatic forces; plasma fluid equations; block-structured locally refined grids; semiconductors; drift-diffusion model; energy equation; Poisson’s equation##### Software:

CVODE
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\textit{P. Colella} et al., J. Comput. Phys. 152, No. 2, 550--583 (1999; Zbl 0954.76062)

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