A Gas-Kinetic Scheme for Maxwell Equations

In this paper, we present a gas-kinetic scheme using discrete velocity space to solve Maxwell equations. The kinetic model recovers Maxwell equations in the zero relaxation time limit. The scheme achieves second-order spatial and temporal accuracy in structured meshes comparable to the finite-difference time-domain (FDTD) method, without requiring staggered grids or leapfrog discretization. Our kinetic scheme is inherently multidimensional due to its use of kinetic beams in multiple directions, allowing larger time steps in multidimensional computations. It demonstrates better stability than FDTD when handling discontinuities and readily extends to unstructured meshes. We validate the method through various test cases including antenna simulation, sphere scattering, and flight vehicle scattering. The results align well with Riemann-solver-based solutions. Finally, we examine charge conservation for Maxwell equations through test cases.