Finite volume methods for numerical simulation of the discharge motion described by different physical models

  • J. Fořt
  • J. Karel
  • D. TrdličkaEmail author
  • F. Benkhaldoun
  • I. Kissami
  • J.-B. Montavon
  • K. Hassouni
  • J. Zs. Mezei


This paper deals with the numerical solution of an ionization wave propagation in air, described by a coupled set of convection-diffusion-reaction equations and a Poisson equation. The standard three-species and more complex eleven-species models with simple chemistry are formulated. The PDEs are solved by a finite volume method that is theoretically second order in space and time on an unstructured adaptive grid. The upwind scheme and the diamond scheme are used for the discretization of the convective and diffusive fluxes, respectively. The Poisson equation is also discretized by the diamond scheme. The results of both models are compared in details for a test case. The influence of physically pertinent boundary conditions at electrodes is also presented. Finally, we deal with numerical accuracy study of implicit scheme in two variants for simplified standard model. It allows us in the future to compute simultaneously and efficiently a process consisting of short time discharge propagation and long-term after-discharge phase or repetitively pulsed discharge.


Discharge propagation Hydrodynamic model Finite volume method Unstructured adaptive mesh 

Mathematics Subject Classification 2010

82D10 74S10 


Funding information

The work was supported by the European Regional Development Fund-Project “Center for Advanced Applied Science” (No. CZ.02.1.01/0.0/0.0/16_019/0000778), and by the Grant Agency of the Czech Technical University in Prague, grant no. SGS19/154/OHK2/3T/12. This research was supported by project LM2018097 funded by the Ministry of Education, Youth and Sports of the Czech Republic, through Zdeněk Bonaventura.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • J. Fořt
    • 1
  • J. Karel
    • 1
  • D. Trdlička
    • 1
    Email author
  • F. Benkhaldoun
    • 2
  • I. Kissami
    • 2
  • J.-B. Montavon
    • 2
  • K. Hassouni
    • 3
  • J. Zs. Mezei
    • 3
    • 4
  1. 1.Department of Technical Mathematics FME CTU in PraguePrague 2Czech Republic
  2. 2.LAGAUniversity Paris 13VilletaneuseFrance
  3. 3.LSPMUniversity Paris 13VilletaneuseFrance
  4. 4.Institute for Nuclear ResearchHungarian Academy of SciencesDebrecenHungary

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