Simulating self-gravitating hydrodynamic flows Original Research Article

An efficient algorithm for solving Poissonʹs equation in two and three spatial dimensions is discussed. The algorithm, which is described in detail, is based on the integral form of Poissonʹs equation and utilizes spherical coordinates and an expansion into spherical harmonics. The solver can be applied to and works well for all problems for which the use of spherical coordinates is appropriate. We also briefly discuss the implementation of the algorithm into hydrodynamic codes which are based on a conservative finite-difference scheme.