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Title: SELF-GRAVITATIONAL FORCE CALCULATION OF SECOND-ORDER ACCURACY FOR INFINITESIMALLY THIN GASEOUS DISKS IN POLAR COORDINATES

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.
Authors:
;  [1] ;  [2]
  1. Institute of Astronomy and Astrophysics, Academia Sinica, P.O. Box 23-141, Taipei 10617, Taiwan, R.O.C. (China)
  2. Department of Mathematics, Fu Jen Catholic University, New Taipei City, Taiwan (China)
Publication Date:
OSTI Identifier:
22520114
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal, Supplement Series; Journal Volume: 221; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCURACY; ALGORITHMS; ANALYTICAL SOLUTION; APPROXIMATIONS; BOUNDARY CONDITIONS; CARTESIAN COORDINATES; FOURIER TRANSFORMATION; GALAXIES; GRAVITATION; GRAVITATIONAL INTERACTIONS; HYDRODYNAMICS; KERNELS; PROTOSTARS; SINGULARITY