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Appl. Sci. 2018, 8(5), 746; https://doi.org/10.3390/app8050746

A Unified Gas Kinetic Scheme for Transport and Collision Effects in Plasma

1
State Key Laboratory of Astronautic Dynamics, Xi’an 710043, China
2
National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi’an 710072, China
*
Author to whom correspondence should be addressed.
Received: 22 March 2018 / Revised: 28 April 2018 / Accepted: 2 May 2018 / Published: 9 May 2018
(This article belongs to the Special Issue Development and Applications of Kinetic Solvers for Complex Flows)
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Abstract

In this study, the Boltzmann equation with electric acceleration term is discretized and solved by the unified gas-kinetic scheme (UGKS). The charged particle transport driven by electric field is included in the electric acceleration term. To capture non-equilibrium distribution function, the probability distribution functions of gas is discretized in a discrete velocity space. After discretization, the numerical flux for distribution function is computed to update the microscopic and macroscopic states. The flux is decided by an integral solution of Boltzmann equation based on characteristic problem. An electron-ion collision model is introduced in the Boltzmann Bhatnagar-Gross-Krook (BGK) equation. This finite volume method for the UGKS couples the free transport and long-range interaction between particles. For simplicity, the electric field induced by charged particles is controlled by the Poisson’s equation, which is solved using the Green’s function for two dimensional plasma system subjected to the symmetry or periodic boundary conditions. Two numerical cases, linear Landau damping and Gaussian beam, are carried out to validate the proposed method. The linear electron plasma wave damping is simulated based on electron-ion collision operator. Comparison results show good accuracy and higher efficiency than particle based methods. Difference between Poisson’s equation and complete electromagnetic Maxwell equation is presented by numerical results based on the two models. Highly non-equilibrium and rarefied plasma flows, such as electron flows driven by electromagnetic field, can be simulated easily. The UGKS-Poisson model is proved to be promising in plasma flow simulation. View Full-Text
Keywords: plasma; Boltzmann equation; unified gas kinetic scheme; Poisson’s equation; finite volume method plasma; Boltzmann equation; unified gas kinetic scheme; Poisson’s equation; finite volume method
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Pan, D.; Zhong, C.; Zhuo, C.; Tan, W. A Unified Gas Kinetic Scheme for Transport and Collision Effects in Plasma. Appl. Sci. 2018, 8, 746.

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