A Discontinuous Galerkin Method for Charged Particle Transport in the Fokker-Planck Limit

A numerical scheme is presented for steady-state, mono-energetic charged particle transport in the Fokker-Planck limit. The spatial domain is meshed into elements, each of which has its own angular mesh. The basis is formed by a discontinuous Galerkin method both in space and in angle. The resulting discretisation is fully arbitrarily refinable in space and angle. No assumptions are made with regards to the shape of the domain. This could form the basis for a deterministic charged particle transport code. A novel approach to spherical diffusion is presented in chapters 2 and 3. It is based on a spherical adaptation of the symmetric interior penalty method. It is developed both for regular discontinuous Galerkin methods and for cell-centred Galerkin finite element methods. Chapter 4 introduces spatial streaming. The weak form is derived. For spatial basis functions of order p, the numerical solution converges with order p+1 as the spatial mesh is refined. It converges to the exact value. That is, there is no approximation other than the Fokker-Planck limit. Other original work includes an analysis of several basis functions on the unit sphere (appendix A) and an overview of numerical integration methods on the unit sphere (appendix B).

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discontinuous Galerkin

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master thesis

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