A high order solver for the unbounded Poisson equation

Hejlesen, Mads Mølholm [Technical University of Denmark] Rasmussen, Johannes Tophøj [Technical University of Denmark] Chatelain, Philippe [UCL] Walther, Jens Honore [Technical University of Denmark]

A high order converging Poisson solver is presented, based on the Greenʼs function solution to Poissonʼs equation subject to free-space boundary conditions. The high order convergence is achieved by formulating regularised integration kernels, analogous to a smoothing of the solution field. The method is extended to directly solve the derivatives of the solution to Poissonʼs equation. In this way differential operators such as the divergence or curl of the solution field can be solved to the same high order convergence without additional computational effort. The method, is applied and validated, however not restricted, to the equations of fluid mechanics, and can be used in many applications to solve Poissonʼs equation on a rectangular unbounded domain.