DUARTE, Max, Zdeněk BONAVENTURA, Marc MASSOT a Anne BOURDON. A numerical strategy to discretize and solve the Poisson equation on dynamically adapted multiresolution grids for time-dependent streamer discharge simulations. Journal of Computational Physics. Elsevier, 2015, roč. 289, MAY, s. 129-148. ISSN 0021-9991. Dostupné z: https://dx.doi.org/10.1016/j.jcp.2015.02.038. |
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@article{1331623, author = {Duarte, Max and Bonaventura, Zdeněk and Massot, Marc and Bourdon, Anne}, article_number = {MAY}, doi = {http://dx.doi.org/10.1016/j.jcp.2015.02.038}, keywords = {Poisson equation; Multiresolution finite volume scheme; Streamer discharges}, language = {eng}, issn = {0021-9991}, journal = {Journal of Computational Physics}, title = {A numerical strategy to discretize and solve the Poisson equation on dynamically adapted multiresolution grids for time-dependent streamer discharge simulations}, url = {http://www.sciencedirect.com/science/article/pii/S0021999115001084}, volume = {289}, year = {2015} }
TY - JOUR ID - 1331623 AU - Duarte, Max - Bonaventura, Zdeněk - Massot, Marc - Bourdon, Anne PY - 2015 TI - A numerical strategy to discretize and solve the Poisson equation on dynamically adapted multiresolution grids for time-dependent streamer discharge simulations JF - Journal of Computational Physics VL - 289 IS - MAY SP - 129-148 EP - 129-148 PB - Elsevier SN - 00219991 KW - Poisson equation KW - Multiresolution finite volume scheme KW - Streamer discharges UR - http://www.sciencedirect.com/science/article/pii/S0021999115001084 L2 - http://www.sciencedirect.com/science/article/pii/S0021999115001084 N2 - 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. ER -
DUARTE, Max, Zdeněk BONAVENTURA, Marc MASSOT a Anne BOURDON. A numerical strategy to discretize and solve the Poisson equation on dynamically adapted multiresolution grids for time-dependent streamer discharge simulations. \textit{Journal of Computational Physics}. Elsevier, 2015, roč.~289, MAY, s.~129-148. ISSN~0021-9991. Dostupné z: https://dx.doi.org/10.1016/j.jcp.2015.02.038.
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