Structure-Preserving Numerical Method for Anisotropic Diffusion Problems in Rarefied Plasmas

Reference No.	2024a040
Type/Category	Grant for General Research-Short-term Joint Research
Title of Research Project	Structure-Preserving Numerical Method for Anisotropic Diffusion Problems in Rarefied Plasmas
Principal Investigator	Rei Kawashima（Department of Electrical Engineering, Shibaura Institute of Technology・Associate Professor）
Research Period	October 29,2024. - October 31,2024.
Keyword(s) of Research Fields	Plasma processing, Ion engine, Plasma simulation, Anisotropic diffusion problem, Mixed finite volume method, Structure-preserving scheme
Abstract for Research Report	Rarefied plasma flows appear in applications such as semiconductor manufacturing equipment and ion engines for space satellites. In these plasma devices, flow control is performed using magnetic fields. However, the flow of strongly magnetized plasma becomes a problem of highly stiff anisotropic diffusion, making it difficult to compute without numerical oscillations. Furthermore, there is an issue that the obtained numerical solutions do not always satisfy the Discrete Maximum Principle (DMP). Research on this issue has been conducted in the field of mathematical sciences for a long time. For example, approaches that convert anisotropic diffusion equations, consisting of second-order derivatives, into a system of first-order hyperbolic equations (hereafter referred to as hyperbolic schemes) have been studied. However, these methods often require careful selection of parameters to satisfy DMP, making them challenging to apply for practical analysis of plasma flow. The aim of this research is to construct a numerical scheme that stably leads to high-quality solutions (here, satisfying DMP) for rarefied plasma flows. After clarifying what characteristics should be preserved to satisfy DMP, we propose a structure-preserving numerical method that calculates the plasma flow with satisfying the conservation characteristics. It is known that the aforementioned hyperbolic schemes can analyze anisotropic diffusion problems stably, despite their simple formulation. This research aims to extend these hyperbolic schemes into a structure-preserving numerical method. Through this research, a new standard in mathematical models and computational methods will be developed for the analysis of rarefied plasma in semiconductor manufacturing processes and space plasma propulsion. By performing accurate numerical calculations on plasma magnetic confinement, flow control, and instability phenomena, we aim to enhance device performance and gain new insights into the physics of magnetized plasma.
Organizing Committee Members (Workshop) Participants (Short-term Joint Usage)	Daisuke Tagami（Institute of Mathematics for Industry, Kyushu University・Associate Professor） Chamarthi Amareshwara Sainadh（Faculty of Mechanical Engineering, Israel Institute of Technology・Postdoctoral Researcher） Tatsuya Sodekoda（Corporate Research and Development, IHI Corporation・Project General Manager）