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A finite volume scheme with limited anti-diffusion for numerical simulation of electric discharges. (English) Zbl 0774.65083

Hyperbolic problems. Theory, numerical methods and applications. Vol. I, Proc. Conf., Uppsala/Sweden 1990, 48-59 (1991).
Summary: [For the entire collection see Zbl 0758.00008.]
A finite volume method with upwinding and limited anti-diffusion is constructed for the numerical study of electric discharges in gas-filled cavities. The ionization term, as well as the convective and diffusive parts of the particle conservation equations, are treated separately, using a fractional step decomposition. The upwinding used for the convective step is corrected by adjunction of an anti-diffusive term controlled by a limiter of the type proposed by S. T. Zalesak [J. Comput. Phys. 31, 335-362 (1979; Zbl 0416.76002)]. This guarantees positivity of the particle densities. Numerical experiments performed with this method are in good agreement with previous results, and show that the method allows to reach much higher densities, for a more accurate simulation of the electric discharge phenomenon.

MSC:

65Z05 Applications to the sciences
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
78A35 Motion of charged particles
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