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A 3D immersed finite element method with non-homogeneous interface flux jump for applications in particle-in-cell simulations of plasma-lunar surface interactions. (English) Zbl 1349.76212

Summary: Motivated by the need to handle complex boundary conditions efficiently and accurately in particle-in-cell (PIC) simulations, this paper presents a three-dimensional (3D) linear immersed finite element (IFE) method with non-homogeneous flux jump conditions for solving electrostatic field involving complex boundary conditions using structured meshes independent of the interface. This method treats an object boundary as part of the simulation domain and solves the electric field at the boundary as an interface problem. In order to resolve charging on a dielectric surface, a new 3D linear IFE basis function is designed for each interface element to capture the electric field jump on the interface. Numerical experiments are provided to demonstrate the optimal convergence rates in \(L^2\) and \(H^1\) norms of the IFE solution. This new IFE method is integrated into a PIC method for simulations involving charging of a complex dielectric surface in a plasma. A numerical study of plasma-surface interactions at the lunar terminator is presented to demonstrate the applicability of the new method.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
65N75 Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
76X05 Ionized gas flow in electromagnetic fields; plasmic flow

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