An innovative Galerkin scheme based on anisotropic trilinear immersed finite elements for the magnetized plasma diffusion problem with plasma sheath interface

Via introducing the Robin flux jump into the Galerkin scheme, this paper develops a new anisotropic trilinear immersed finite element (IFE) method for solving the magnetized plasma diffusion problem with plasma sheath interface condition under Cartesian meshes. The three-dimensional (3D) diffusion process of magnetized plasma is anisotropic and highly sensitive to magnetic fields, making it difficult to efficiently solve by commonly used body fitted mesh methods when the simulation domain has complex boundary conditions. Even worse, the plasma sheath boundary will further exacerbates its solving difficulty. The presented method first utilizes the anisotropic trilinear IFE basis functions describing the diffusion of magnetized plasma in interface elements. Then the trilinear IFE basis functions are used to handle the plasma sheath interface conditions, i.e. the Robin flux jump conditions. As for the other non interface elements, the traditional trilinear basis functions are used. On this basis, a new Galerkin scheme is derived and applied to efficiently solving the plasma anisotropic diffusion problem with the Robin flux jump interfaces in Cartesian meshes. The proposed method can also solve other types of elliptical interface problems via controlling the coefficients. Moreover, the orthogonal meshes makes it convenient to couple other Cartesian mesh based methods, such as the particle-in-cell method, which provides an advanced tool for solving plasma transport problems. Numerical experiments are provided to demonstrate the proposed method and show the applicability in the simulations of actual engineering issues.