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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Publikace nespadá pod Filozofickou fakultu, ale pod Přírodovědeckou fakultu. Oficiální stránka publikace je na webu muni.cz.
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DUARTE Max BONAVENTURA Zdeněk MASSOT Marc BOURDON Anne

Rok publikování 2015
Druh Článek v odborném periodiku
Časopis / Zdroj Journal of Computational Physics
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www http://www.sciencedirect.com/science/article/pii/S0021999115001084
Doi http://dx.doi.org/10.1016/j.jcp.2015.02.038
Obor Fyzika plazmatu a výboje v plynech
Klíčová slova Poisson equation; Multiresolution finite volume scheme; Streamer discharges
Popis 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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