A numerical strategy to discretize and solve the Poisson equation on dynamically adapted multiresolution grids for time-dependent streamer discharge simulations

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Authors

DUARTE Max BONAVENTURA Zdeněk MASSOT Marc BOURDON Anne

Year of publication 2015
Type Article in Periodical
Magazine / Source Journal of Computational Physics
MU Faculty or unit

Faculty of Science

Citation
Web http://www.sciencedirect.com/science/article/pii/S0021999115001084
Doi http://dx.doi.org/10.1016/j.jcp.2015.02.038
Field Plasma physics
Keywords Poisson equation; Multiresolution finite volume scheme; Streamer discharges
Description We develop a numerical strategy to solve multi-dimensional Poisson equations on dynamically adapted grids for evolutionary problems disclosing propagating fronts. The method is an extension of the multiresolution finite volume scheme used to solve hyperbolic and parabolic time-dependent PDEs. Such an approach guarantees a numerical solution of the Poisson equation within a user-defined accuracy tolerance. Most adaptive meshing approaches in the literature solve elliptic PDEs level-wise and hence at uniform resolution throughout the set of adapted grids. Here we introduce a numerical procedure to represent the elliptic operators on the adapted grid, strongly coupling inter-grid relations that guarantee the conservation and accuracy properties of multiresolution finite volume schemes. The discrete Poisson equation is solved at once over the entire computational domain as a completely separate process. The accuracy and numerical performance of the method are assessed in the context of streamer discharge simulations.
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