A Gas-Kinetic Scheme for Maxwell Equations

TL;DR

This paper introduces a novel gas-kinetic scheme for Maxwell's equations that achieves second-order accuracy, lower numerical dissipation, and better boundary condition handling, suitable for complex electromagnetic simulations.

Contribution

It extends the gas-kinetic scheme to electromagnetic problems using a discrete velocity space and demonstrates advantages over classical methods in accuracy and boundary treatment.

Findings

Achieves second-order accuracy in electromagnetic simulations.

Exhibits lower numerical dissipation compared to classical FVS methods.

Successfully models electromagnetic wave propagation in complex geometries.

Abstract

The Gas-Kinetic Scheme (GKS), widely used in computational fluid dynamics for simulating hypersonic and other complicated flow phenomena, is extended in this work to electromagnetic problems by solving Maxwell's equations. In contrast to the classical GKS formulation, the proposed scheme employs a discrete rather than a continuous velocity space. By evaluating a time-accurate numerical flux at cell interfaces, the proposed scheme attains second-order accuracy within a single step. Its kinetic formulation provides an inherently multidimensional framework, while the finite-volume formulation ensures straightforward extension to unstructured meshes. Through the incorporation of a collision process, the scheme exhibits lower numerical dissipation than classical flux-vector splitting (FVS) methods. Furthermore, the kinetic decomposition enables direct implementation of non-reflecting boundary conditions. The proposed scheme is validated against several benchmark problems and compared with established methods, including the Finite-Difference Time-Domain (FDTD) method and FVS. A lattice Boltzmann method (LBM) implementation is also included for comparative analysis. Finally, the technique is applied to simulate electromagnetic wave propagation in a realistic aircraft configuration, demonstrating its ability to model complex geometries.