Self-gravitational force calculation of second-order accuracy for infinitesimally thin gaseous disks in polar coordinates

Hsiang Hsu Wang, David C.C. Yen, Ronald E. Taam

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish (US)
Article number4
JournalAstrophysical Journal, Supplement Series
Issue number1
StatePublished - Nov 1 2015


  • gravitation
  • methods: numerical

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


Dive into the research topics of 'Self-gravitational force calculation of second-order accuracy for infinitesimally thin gaseous disks in polar coordinates'. Together they form a unique fingerprint.

Cite this