1. A new numerical strategy with space-time adaptivity and error control for multi-scale streamer discharge simulations
- Author
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Zdenk Bonaventura, Anne Bourdon, Marc Massot, Max Duarte, Stéphane Descombes, Thierry Dumont, Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion (EM2C), Université Paris Saclay (COmUE)-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec, Department of Physical Electronics, Masaryk University [Brno] (MUNI), Laboratoire Jean Alexandre Dieudonné (JAD), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), and This research was supported by a fundamental project grant from ANR (French National Research Agency - ANR Blancs): Séchelles} (project leader S. Descombes), and by a DIGITEO RTRA project: MUSE (project leader M. Massot). The support of a Ph.D. grant from Mathematics (INSMI) and Engineering (INSIS) Institutes of CNRS is gratefully acknowledged ad well as the the support by INCA project (National Initiative for Advanced Combustion - CNRS - ONERA - SAFRAN). Support of Ecole Centrale Paris is gratefully acknowledged for several month stay of Z. Bonaventura at Laboratory EM2C as visiting Professor. Z. Bonaventura is also grateful to the Ministry of Education, Youth and Sports of the Czech Republic under project CZ.1.05/2.1.00/03.0086 and project MSM 0021622411.
- Subjects
Physics and Astronomy (miscellaneous) ,Scale (ratio) ,Computation ,FOS: Physical sciences ,Streamer discharge ,01 natural sciences ,Stability (probability) ,010305 fluids & plasmas ,[PHYS.PHYS.PHYS-COMP-PH]Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph] ,time adaptive integration ,[PHYS.PHYS.PHYS-PLASM-PH]Physics [physics]/Physics [physics]/Plasma Physics [physics.plasm-ph] ,Control theory ,Physics::Plasma Physics ,0103 physical sciences ,FOS: Mathematics ,Mathematics - Numerical Analysis ,Simulation ,space adaptive multiresolution : error control ,010302 applied physics ,Physics ,Numerical Analysis ,Spacetime ,Applied Mathematics ,Numerical analysis ,Space time ,[SPI.PLASMA]Engineering Sciences [physics]/Plasmas ,MSC 65M08, 65M50, 65Z05, 65G20 ,Numerical Analysis (math.NA) ,Computational Physics (physics.comp-ph) ,multi-scale plasma discharge ,Physics - Plasma Physics ,Computer Science Applications ,Plasma Physics (physics.plasm-ph) ,Computational Mathematics ,Nonlinear system ,Modeling and Simulation ,Physics - Computational Physics ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Abstract
This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma discharges, considering drift-diffusion equations and the computation of electric field. The proposed numerical method provides a time-space accuracy control of the solution, and thus, an effective accurate resolution independent of the fastest physical time scale. An important improvement of the computational efficiency is achieved whenever the required time steps go beyond standard stability constraints associated with mesh size or source time scales for the resolution of the drift-diffusion equations, whereas the stability constraint related to the dielectric relaxation time scale is respected but with a second order precision. Numerical illustrations show that the strategy can be efficiently applied to simulate the propagation of highly nonlinear ionizing waves as streamer discharges, as well as highly multi-scale nanosecond repetitively pulsed discharges, describing consistently a broad spectrum of space and time scales as well as different physical scenarios for consecutive discharge/post-discharge phases, out of reach of standard non-adaptive methods., Comment: Support of Ecole Centrale Paris is gratefully acknowledged for several month stay of Z. Bonaventura at Laboratory EM2C as visiting Professor. Authors express special thanks to Christian Tenaud (LIMSI-CNRS) for providing the basis of the multiresolution kernel of MR CHORUS, code developed for compressible Navier-Stokes equations (D\'eclaration d'Invention DI 03760-01). Accepted for publication; Journal of Computational Physics (2011) 1-28
- Published
- 2011
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