A Multiscale Approach Using Patches of Finite Elements for Solving Wave Propagation Problems in Microwave Discharge Plasma

Emanuele Arcese,Jean-Pierre Boeuf,François Rogier

doi:10.3389/fphy.2019.00026

Abstract

We consider the development of an efficient numerical method for the simulation of microwave discharge plasmas. The method uses the idea of finite element patch and can deal with very disparate length scales of the plasma. In this paper, the time-domain Maxwell's equations, which are coupled with the plasma transport equations via the time-varying electron current density, are solved with a two-level Schwarz type algorithm based on a variational formulation of the standard Yee scheme. The patch of finite elements is used to calculate in an iterative manner the solution in the plasma region where a better precision is required. This numerical approach provides the Yee scheme with an efficient local-grid refinement capacity while preserving its stability. A numerical analysis shows its accuracy and computational efficiency on nested Cartesian grids. Simulation of a microwave breakdown in air under atmospheric pressure is then performed and results are discussed. We believe that both the inherent versatility with regard to the variational formulation and the efficiency of the proposed method can make it particularly suitable in modeling of microwave discharge plasmas by providing more insights of their nature and behavior.

Highlights

There is an increasing interest of microwave plasma sources at atmospheric pressure for medicine, waste treatment and for aeronautic and space applications
We assess the efficiency of the proposed multiscale method for the wave propagation problem in microwave discharge plasma
We have proposed a new method for numerically solving electromagnetic wave propagation problems in plasma having a strong multiscale behavior such as the microwave discharge plasma modeling

Summary

Introduction

There is an increasing interest of microwave plasma sources at atmospheric pressure for medicine, waste treatment and for aeronautic and space applications. Energy deposition by microwave discharges has received significant interest in the past several decades as a promising technique for aerodynamic flow control at high speed or plasma assisted combustion [1]. Recent experiences [2] have shown a dramatic reduction of the surface pressure coefficients due to the strong interaction of a microwave discharge with a Mach 3 incoming flow. Properties of microwave plasma are used in the plasma arrays with 2-D periodicity producing frequency regions of forbidden propagation like band gaps in a photonic crystal [4]

Methods

Results

Conclusion