**Topic/Type**:
1. Plasma Simulation, Poster

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Mathematical Modeling on Electrostatic Model of Dielectric Barrier Discharge

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J. Labadin**^{1}, A. Ahmadi^{1}, P. Phang^{1}, A. R. H. Rigit^{2}

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*^{1} Department of Computational Science and Mathematics, FCSIT, Universiti Malaysia Sarawak

^{2} Department of Mechanical Engineering, FEng, Universiti Malaysia Sarawak

Dielectric Barrier Discharge is a discharge phenomenon where a high voltage is applied on at least two electrodes and the electrodes was insulated by at least one dielectric material. Dielectric Barrier Discharge plasma actuator has been studied widely in this last decade but mostly the study is focusing on experimental research rather than modeling the problem mathematically. The limitation with studying Dielectric Barrier Discharge plasma actuator experimentally is it does not obtain direct information on the physics of the plasma flow, which is important in order to increase the efficiency of the plasma actuator itself. In this paper, we will model the electrostatics aspects of the Dielectric Barrier Discharge plasma actuator mathematically. This is the first part in modeling the plasma flow, and this preliminary result of the model will be presented and discussed in this paper. To initiate the modeling process, the Maxwell?s equations are used and a few assumptions are made, which lead to only one differential equation. Then, Debye length is introduced and Coulomb force is applied in order to make this model more realistic. Finally, a system of equations with three unknowns electrical potential φ, electrical field E and electrostatics field fb together with their corresponding boundary conditions are obtained. In the numerical formulation part, coordinate transformation is applied to the governing equations so that they are represented into a mathematical uniform grid. Then, discretization using centered finite difference method is performed in order to transform the continuous equation into discrete equation. The equation is then solved using Gauss-Seidel iteration method ensuring all the mentioned boundary conditions are fulfilled. The numerical results of this model are represented into a contour image of φ, E and fb. Comparison is made between the different values of applied voltage on the upper electrode. From this simple model, we found that the higher the applied voltage is the higher the magnitude of the electrical and electrostatic field. In other words, we conclude that the applied voltage have significant influence on the electrical and electrostatics field.