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

J 2015

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

DUARTE, Max, Zdeněk BONAVENTURA, Marc MASSOT and Anne BOURDON

Basic information

Original name

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

Authors

DUARTE, Max (600 Paraguay), Zdeněk BONAVENTURA (203 Czech Republic, guarantor, belonging to the institution), Marc MASSOT (250 France) and Anne BOURDON (250 France)

Edition

Journal of Computational Physics, Elsevier, 2015, 0021-9991

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10305 Fluids and plasma physics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 2.556

RIV identification code

RIV/00216224:14310/15:00086125

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1016/j.jcp.2015.02.038

UT WoS

000351081000009

Keywords in English

Poisson equation; Multiresolution finite volume scheme; Streamer discharges

Abstract

V originále

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.

Links

ED2.1.00/03.0086, research and development project

Name: Regionální VaV centrum pro nízkonákladové plazmové a nanotechnologické povrchové úpravy

Citovat

DUARTE, Max, Zdeněk BONAVENTURA, Marc MASSOT and 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, vol. 289, MAY, p. 129-148. ISSN 0021-9991. Available from: https://dx.doi.org/10.1016/j.jcp.2015.02.038.

@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 and 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, vol.~289, MAY, p.~129-148. ISSN~0021-9991. Available from: https://dx.doi.org/10.1016/j.jcp.2015.02.038.

Detailed Information on Publication Record