A high order solver for the unbounded Poisson equation

Authors:
Mads Mølholm Hejlesen;Johannes Tophøj Rasmussen;Philippe Chatelain;Jens Honoré Walther
Affiliations:
Department of Mechanical Engineering, Technical University of Denmark, Building 403, DK-2800 Kgs. Lyngby, Denmark;Department of Mechanical Engineering, Technical University of Denmark, Building 403, DK-2800 Kgs. Lyngby, Denmark;Institute of Mechanics, Materials and Civil Engineering, Université catholique de Louvain, B-1348, Belgium;Department of Mechanical Engineering, Technical University of Denmark, Building 403, DK-2800 Kgs. Lyngby, Denmark and Computational Science and Engineering Laboratory, ETH Zürich, Clasiusstra ...
Venue:
Journal of Computational Physics
Year:
2013

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Abstract

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.