A three-dimensional finite-volume solver for the Maxwell equations with divergence cleaning on unstructured meshes Original Research Article

A finite-volume scheme on unstructured meshes for the three-dimensional time-dependent Maxwell equations is presented. To avoid the increase of numerical errors caused by suppressing the information contained in Gaussʹ law as well as the divergence-free condition of the magnetic induction, a divergence cleaning step is added which does not require the solution of a Poisson equation. The elliptical constraints of the Maxwell equations is approximated by a hyperbolic condition, starting from the so-called Generalised Lagrange Multiplier Maxwell model. This results in a purely hyperbolic system that fits very well in the framework of high-resolution finite-volume schemes yielding an efficient and flexible parallel Maxwell solver for explicit field calculations in time domain on unstructured grids in three space dimensions. Simulation results obtained with this new approximation technique are presented and compared with analytical as well as with other methods.