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Keywords = flux corrected transport (FCT)

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19 pages, 4616 KB  
Article
Modeling Streamer Discharge in Air Using Implicit and Explicit Finite Difference Methods with Flux Correction
by Hasupama Jayasinghe, Liliana Arevalo, Richard Morrow and Vernon Cooray
Plasma 2025, 8(2), 21; https://doi.org/10.3390/plasma8020021 - 29 May 2025
Cited by 1 | Viewed by 2419
Abstract
Implementing a computationally efficient numerical model for a single streamer discharge is essential to understand the complex processes such as lightning initiation and electrical discharges in high voltage systems. In this paper, we present a streamer discharge simulation in air, by solving one-dimensional [...] Read more.
Implementing a computationally efficient numerical model for a single streamer discharge is essential to understand the complex processes such as lightning initiation and electrical discharges in high voltage systems. In this paper, we present a streamer discharge simulation in air, by solving one-dimensional (1D) drift diffusion reaction (DDR) equations for charged species with the disc approximation for electric field. A recently developed fourth-order space and time-centered implicit finite difference method (FDM) with a flux-corrected transport (FCT) method is applied to solve the DDR equations, followed by a comparative simulation using the well-established explicit FDM with FCT. The results demonstrate good agreement between implicit and explicit FDMs, verifying their reliability for streamer modeling. The total electrons, total charge, streamer position, and hence the streamer bridging time obtained using the FDMs with FCT agree with the same streamer computed in the literature using different numerical methods and dimensions. The electric field is obtained with good accuracy due to the inclusion of image charges representing the electrodes in the disc method. This accuracy can be further improved by introducing more image charges. Both implicit and explicit FDMs effectively capture the key streamer behavior, including the variations in charged particle densities and electric field. However, the implicit FDM is computationally more efficient. Full article
(This article belongs to the Special Issue Recent Advances of Dielectric Barrier Discharges)
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8 pages, 1370 KB  
Article
An Implicit Flux-Corrected Transport Algorithm Used for Gas Discharge Calculations
by Richard Morrow
Plasma 2025, 8(1), 7; https://doi.org/10.3390/plasma8010007 - 28 Feb 2025
Cited by 1 | Viewed by 1114
Abstract
An implicit flux-corrected transport (FCT) and diffusion algorithm was developed and used in many gas discharge calculations. Such calculations require the use of a fine mesh where the electric field changes rapidly; that is, near electrodes or in a streamer front. If diffusion [...] Read more.
An implicit flux-corrected transport (FCT) and diffusion algorithm was developed and used in many gas discharge calculations. Such calculations require the use of a fine mesh where the electric field changes rapidly; that is, near electrodes or in a streamer front. If diffusion is included using an explicit method, then the von Neumann stability condition severely limits the time-step that can be used; however, this limitation does not apply to implicit methods. Further, for gas discharge calculations including space-charge effects, it is necessary to solve the continuity equations with no negative number densities nor point-by-point oscillation in the number density. This is because the electron number densities are finely balanced with the ion number densities to determine the space-charge distribution and hence the electric field which drives the motion of the particles. An efficient way to solve the particle transport equation, with the required properties, is to use FCT. The most accurate form of FCT developed by the author is implicit fourth-order FCT; hence, the method presented incorporates implicit diffusion into the implicit fourth-order FCT scheme to produce a robust algorithm that has been successfully used in many calculations. Full article
(This article belongs to the Special Issue Recent Advances of Dielectric Barrier Discharges)
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18 pages, 2387 KB  
Article
A Finite Element Flux-Corrected Transport Method for Wave Propagation in Heterogeneous Solids
by Stefano Mariani, Roberto Martini and Aldo Ghisi
Algorithms 2009, 2(1), 1-18; https://doi.org/10.3390/a2010001 - 13 Jan 2009
Cited by 9 | Viewed by 9907
Abstract
When moving discontinuities in solids need to be simulated, standard finite element (FE) procedures usually attain low accuracy because of spurious oscillations appearing behind the discontinuity fronts. To assure an accurate tracking of traveling stress waves in heterogeneous media, we propose here a [...] Read more.
When moving discontinuities in solids need to be simulated, standard finite element (FE) procedures usually attain low accuracy because of spurious oscillations appearing behind the discontinuity fronts. To assure an accurate tracking of traveling stress waves in heterogeneous media, we propose here a flux-corrected transport (FCT) technique for structured as well as unstructured space discretizations. The FCT technique consists of post-processing the FE velocity field via diffusive/antidiffusive fluxes, which rely upon an algorithmic length-scale parameter. To study the behavior of heterogeneous bodies featuring compliant interphases of any shape, a general scheme for computing diffusive/antidiffusive fluxes close to phase boundaries is proposed too. The performance of the new FE-FCT method is assessed through one-dimensional and two-dimensional simulations of dilatational stress waves propagating along homogeneous and composite rods. Full article
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