A Self-gravity Module for the PLUTO Code

We present a novel implementation of an iterative solver for the solution of Poisson's equation in the PLUTO code for astrophysical fluid dynamics. Our solver relies on a relaxation method in which convergence is sought as the steady-state solution of a parabolic equation, whose time discretization is governed by the Runge-Kutta-Legendre (RKL) method. Our findings indicate that the RKL-based Poisson solver, which is both fully parallel and rapidly convergent, has the potential to serve as a practical alternative to conventional iterative solvers such as the Gauss-Seidel and successive overrelaxation methods. Additionally, it can mitigate some of the drawbacks of these traditional techniques. We incorporate our algorithm into a multigrid solver to provide a simple and efficient gravity solver that can be used to obtain the gravitational potentials in self-gravitational hydrodynamics. We test our implementation against a broad range of standard self-gravitating astrophysical problems designed to examine different aspects of the code. We demonstrate that the results match excellently with analytical predictions (when available), and the findings of similar previous studies.