A Combined Immersed Finite Element and Conservative Semi-Lagrangian Scheme for Plasma-Material Interactions

Abstract

In this paper, the immersed finite element (IFE) coupled with the conservative semi-Lagrangian (CSL) kinetic scheme is developed for plasma-material interactions. The proposed method (IFE-CSL) enjoys respective advantages of the IFE and CSL, i.e, the flexibility and efficiency for treating complex boundary conditions, mass conservation and being free from the Courant-Friedrichs-Lewy (CFL) condition. In the current IFE-CSL, the IFE method based on structured interface-independent meshes is developed for the spatial discretization of the field equation, which provides an accurate approach with convenient implementations to solve the field problems with irregular interface. The CSL scheme combined with an immersed method termed half-way ghost-cell is proposed for the spatial discretization of the Vlasov equation, which enables the proposed method to exactly conserve mass and conveniently handle curved boundaries. Then the IFE and CSL method are coupled via the charge density depending on full kinetic or hybrid kinetic model, where the appropriate IFE solver is developed for the linear or nonlinear Poisson equation, respectively. In the current IFE-CSL, different geometries can be treated automatically for both IFE and CSL through the specific geometric information. As a result, the proposed CSL-IFE can be conveniently and efficiently applied to simulate the plasma-material interactions with structured interface-independent meshes. Finally, several numerical experiments are performed to demonstrate the capabilities of the proposed method.

Keywords: semi-Lagrangian scheme, immersed finite element, Vlasov-Possion system, plasma-material interactions.