A high order solver for the unbounded Poisson equation

A high order converging Poisson solver is presented, based on the Green's function solution to Poisson's 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 Poisson's 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 Poisson's equation on a rectangular unbounded domain. (C) 2013 Elsevier Inc. All rights reserved.