A Godunov-type solver for the Maxwell equations with divergence cleaning

We present a high-resolution finite-volume Godunov-type Maxwell solver for three-dimensional unstructured meshes, based on the purely hyperbolic Maxwell (PHM) system, which is established by introducing two additional degrees of freedom into the evolutionary part of the Maxwell equations and coupling them with the elliptical constraints given by Gauss' law and the del (.) B = 0 statement. This model allows for possible errors in the charge conservation equation as may occur in particle-in-cell simulations, and yields approximative solutions of the conventional Maxwell equations. Numerical results demonstrate the relevance of the correction approach when the charge conservation equation is violated.