In this article, an analytical-numerical approach to calculating a stationary thermal field in the elliptical region is presented. The eigenfunctions of the Laplace operator were determined analytically, whereas the coefficients of the eigenfunctions were obtained numerically. The cooling was modeled with 3rd kind (Hankel’s) boundary condition, where the total heat transfer coefficient was the sum of the convective and radiative components. The method was used to analyze the thermal field in an elliptical conductor and a dielectrically heated elliptical column. The basic parameters of these systems, i.e. their steady-state current rating and the maximum charge temperature, were determined. The results were verified using the finite element method and have been presented graphically.
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In this manuscript, both electric and energy behavior of a 2D spatial distributions in the Cartesian geometry of electron, ion and total longitudinal current densities as well as both ionization and energy sources terms of a DC glow discharge in the normal mode and in low gas pressure are presented for the first time in the literature. The model used in this work is the second order fluid model (continuity and momentum transfer equations and energy equation for electrons). The set of equations are coupled in a self-consistent way with Poisson’s equation. The results obtained in the stationary state are in good agreement with those given by literature.
PL
Analizowany jest prąd wyładowania DC i określany jest przestrzenny rozkład strumienia elektronów, jonów, prądu a także pokreślone są źródła energii jonizacji. Jako model do analizy przyjęto model płynu drugiego rzędu. Równania są sprzężone z odpowiednimi równaniami Poissona.
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In this paper, we have developed a tri-dimensional numerical modelling of filamentary discharge, which enabled us to study the streamer discharge's propagation at high pressure, in a uniform electrical field. The transport equations and Poisson's equation formed self-consistent model. We use Scharfetter and Gummel schemes SG and SG0 coupling at time splitting method to resolve the transport equations system. The Poisson's equation is resolved by the tri- diagonal method coupled with the over-relaxation method to calculate the electrical field.
PL
W artykule opisano budowę modelu 3-D wyładowania włókienkowego, który posłużył do badań propagacji wyładowania wstęgowego przy wysokim ciśnieniu w jednorodnym polu elektrycznym. Model oparty jest na równaniach Poisson’a i transportu. W celu rozwiązania równań transportu, zastosowano metodę sprzężenia SG i SG0 Scharfetter’a i Gummela, natomiast do formuły Poisson’a zastosowano metodę tridiagonalną, w połączeniu z metodą SOR (ang. Successive Over-Relaxation method).
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This paper deals with the distribution of electric scalar potential within an infinitely long electrodes system the cross section of which is a circular annulus. We provide guidelines about an efficient method for solving a wide class of electrostatic problems.
PL
W artykule omówiono zagadnienie rozkładu potencjału elektrycznego na nieskończenie długich elektrodach, modelujących pierścień kołowy. Przedstawiono sposoby rozwiązywania zagadnień elektrostatyki, dotyczącej danego przypadku.
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The paper deals with an interval difference method for solving the Poisson equation based on the conventional central-difference method. We present the interval method in full details. The method is constructed in such a way that the exact solution is included in the interval solution obtained. Some numerical results obtained in floating-point interval arithmetic are also presented
Particle-in-cell (PIC) technique is a widely used computational method in the simulation of low density collisionless plasma flows. In this study, a new two-dimensional (2-D) electrostatic particle-in-cell solver is developed that can be applied to non-rectangular configurations.
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This paper describes the application of the method of fundamental solutions to the solution of the boundary value problems of the two-dimensional steady heat transfer with heat sources. For interpolation of an inhomogeneous term in Poisson equation the radial basis functions are used. Three cases of boundary value problems are solved and five cases of radial basis functions are used. For comparison purposes the boundary value problems for which exact solution exists were chosen. Application of method of fundamental solutions with boundary collocation and radial basis function for solution of inhomogeneous boundary value problems introduces some number of parameters related with these tools. For optimal choosing of these parameters the genetic algorithm is used. The results of numerical experiences related to optimal parameters are presented.
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In this paper the variant of the boundary element method called dual reciprocity BEM is presented. On the stage of numerical computations the DRBEM application for the Poisson equation allows to avoid the discretization of the interior of the domain considered. In the final part of the paper the results of computations are shown.
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