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

• Published in: Advances in computational mathematics Vol. 45; no. 4; pp. 2163 - 2189
• Main Authors: Fořt, J., Karel, J., Trdlička, D., Benkhaldoun, F., Kissami, I., Montavon, J.-B., Hassouni, K., Mezei, J. Zs
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-08-2019; Springer Nature B.V; Springer Verlag
• Subjects: Boundary conditions; Computational mathematics; Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Computer simulation; Convection; Diamonds; Discharge; Discretization; Finite volume method; Fluxes; Ionization waves; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Numerical Analysis; Numerical methods; Organic chemistry; Poisson equation; Reaction-diffusion equations; Visualization; Wave propagation; Hydrodynamic model; Finite volume method; Discharge propagation; 74S10; Unstructured adaptive mesh; 82D10
• ISSN: 1019-7168; 1572-9044
• DOI: 10.1007/s10444-019-09706-9

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.