Self-Gravitational Force Calculation of Infinitesimally Thin Gaseous Disks on Nested Grids

TL;DR

This paper develops a second-order, fast, and boundary-condition-free method for calculating the self-gravitational forces in infinitesimally thin gaseous disks using nested grids, verified for accuracy and efficiency.

Contribution

It introduces a novel second-order formula and a Fourier-based numerical technique for efficient self-gravity computation on nested grids for thin disks.

Findings

Method achieves second-order accuracy.

Computational complexity is nearly linear.

Applicable to planetary migration and galaxy morphology studies.

Abstract

We extend the work of Yen et al. (2012) and develop 2nd order formulae to accommodate a nested grid discretization for the direct self-gravitational force calculation for infinitesimally thin gaseous disks. This approach uses a two-dimensional kernel derived for infinitesimally thin disks and is free of artificial boundary conditions. The self-gravitational force calculation is presented in generalized convolution forms for a nested grid configuration. A numerical technique derived from a fast Fourier transform is employed to reduce the computational complexity to be nearly linear. By comparing with analytic potential-density pairs associated with the generalized Maclaurin disks, the extended approach is verified to be of second order accuracy using numerical simulations. The proposed method is accurate, computationally fast and has the potential to be applied to the studies of planetary migration and the gaseous morphology of disk galaxies.