Study on numerical diffuson in aligned and non-aligned meshes for magnetically confined plasma transport equations

Abstract

One of the main challenges present in the numerical modeling of magnetically confined plasmas is due to the highly anisotropic nature of these systems. In certain electric propulsion engines, such as electromagnetic thrusters, plasma discharges occur under complex magnetic field configurations, which requires the use of appropriate computational meshes to precisely simulate the behaviour of the plasma and obtain the least numerical error. This Bachelor Thesis is devoted to estimating the numerical error induced when posing the anisotropic plasma diffusion equation in structured, unaligned meshes, in order to address the benefits derived from the use of Magnetic Field-Aligned Meshes (MFAMs) in highly anisotropic problems. It is discussed whether typical discretization errors due to gradient reconstruction methods and low quality mesh elements in MFAMs are comparable to those induced by numerical diffusion in unaligned meshes. First, the evolution of a highly anisotropic system in a computational mesh unaligned with the magnetic eld is analyzed. By means of an average error, numerical di usion will be quantified attending to different parameters: mesh refinement, magnetic field misalignment, geometric mesh quality, and various anisotropicity levels. Furthermore, a qualitative analysis is performed to show how these factors contribute to numerical diffusion. Then, a benchmark comparison of the evolution of a highly anisotropic problem in a strcutured, non-aligned mesh against the solution in a MFAM is provided. Additionally, errors due to gradient reconstruction in the non-structured MFA mesh are discussed. It is concluded that, in spite of the errors that may arise due to gradient reconstruction methods or low geometric mesh quality regions, Magnetic Field-Aligned Meshes provide with a more correct approach in the modeling of highly anisotropic systems, specially if the anisotropicity level is not known a-priori.