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Title: Numerical Methods and Comparison for Simulating Long Streamer Propagation
Keywords: streamer propagations,hyperbolic system,coupling with elliptic equation,DG methods,mixed finite element method,least-squares finite element method
Issue Date: 3-Jul-2014
Citation: HUANG MENGMIN (2014-07-03). Numerical Methods and Comparison for Simulating Long Streamer Propagation. ScholarBank@NUS Repository.
Abstract: In plasma physics, streamer propagation is an interesting discharge phenomenon which has many applications in engineering and industry. Due to the small time scale of streamer propagation, numerical simulation becomes a more effective way to study the streamer than experiment. The governing partial differential equations (PDEs) of streamer propagation include continuity equations for the particle densities coupled with a Poisson's equation for the electric potential. In this thesis, two discontinuous Galerkin (DG) methods are proposed to solve the continuity equations since there are large derivatives or even jumps in the profile of particle densities. Meanwhile, the Poisson's equation is solved by 4 different methods which include finite difference method (FDM), mixed finite element method (MFEM), least-squares finite element method (LSFEM), and symmetric interior penalty Galerkin (SIPG) method. We have compared the compatibility when these 4 methods are coupled with DG methods for continuity equations. The comparison results recommend that FDM is the best method for Poisson's equations if uniform rectangular meshes are used and SIPG method is the best choice for triangular meshes. By applying the recommended methods, we have simulated many configurations of short and long streamer propagations and successfully captured the features of streamer. In summary, this thesis work is a comprehensive study in applying DG methods to numerical simulations of streamer propagations. It supplements some early numerical studies done by our collaborators. The gap lengths in most of the simulations in our study are 5 times longer as the existing results, hence we have observed more interesting phenomenon during simulations, for example the bifurcation of streamer. We have considered not only the rectangular computational domain in this thesis, but also carried out simulation in complex geometry. Our study indicates that DG method are highly potential competitor in simulating streamer propagations. In addition, this work studies the numerical compatibility in the coupling between hyperbolic system and elliptic equation.
Appears in Collections:Ph.D Theses (Open)

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