2015/09/04 by Hsiang-Hsu Wang, David C. C. Yen, Ronald E. Taam
Physics and Astronomy · #Astronomy and Astrophysical Research #Boundary (topology) #Cartesian coordinate system #Convolution (computer science) #Eigenfunction #Galaxies: Formation, Evolution, Phenomena #Infinitesimal #Poisson kernel #Polar #Polar coordinate system #Singularity #Stellar, planetary, and galactic studies #astro-ph.IM
paper · pdf · doi:10.1088/0067-0049/221/1/4
35 pages, 7 figures, accepted for publication in ApJS
arxiv created 2015/09/04 · openalex publication_date 2015/10/06 · arxiv updated 2015/10/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
Investigating the evolution of disk galaxies and the dynamics of proto-stellar disks can involve the use of both a hydrodynamical and a Poisson solver. These systems are usually approximated as infinitesimally thin disks using two-dimensional Cartesian or polar coordinates. In Cartesian coordinates, the calculations of the hydrodynamics and self-gravitational forces are relatively straightforward for attaining second-order accuracy. However, in polar coordinates, a second-order calculation of self-gravitational forces is required for matching the second-order accuracy of hydrodynamical schemes. We present a direct algorithm for calculating self-gravitational forces with second-order accuracy without artificial boundary conditions. The Poisson integral in polar coordinates is expressed in a convolution form and the corresponding numerical complexity is nearly linear using a fast Fourier transform. Examples with analytic solutions are used to verify that the truncated error of this algorithm is of second order. The kernel integral around the singularity is applied to modify the particle method. The use of a softening length is avoided and the accuracy of the particle method is significantly improved.