A fully decoupled iterative method with three-dimensional anisotropic immersed finite elements for Kaufman-type discharge problems

Abstract

In order to simulate the Kaufman-type discharge problems, a fully decoupled iterative method with anisotropic immersed finite elements on Cartesian meshes is proposed, especially for a three-dimensional (3D) non-axisymmetric anisotropic hybrid model which is more difficult than the axisymmetric or isotropic models. The classical hybrid model, which describes the important plasma distribution of the Kaufman-type discharge problems, couples several difficult equations together to form a large scale system. The 3D non-axisymmetric and anisotropic properties will further increase the complexity of this system. Hence it generally needs to be solved in the decoupled way for significantly reducing the computational cost. Based on the Particle-in-Cell Monte Carlo collision (PIC–MCC) method and the immersed finite element (IFE) method, we propose a fully decoupled iterative method for solving this complex system. The IFE method allows Cartesian meshes for general interface problems, while the traditional finite element methods require body-fitting meshes which are often unstructured. Compared with traditional finite element methods, this feature significantly improves the efficiency of the proposed 3D fully decoupled iterative method, while maintaining the optimal accuracy of the chosen finite elements. Numerical simulations of traditional Kaufman ion thruster and annular ion thruster discharge chambers are provided and compared with the corresponding lab experiment results to illustrate the features of the proposed method.