Hyperbolic Self-Gravity Solver for Large Scale Hydrodynamical Simulations

TL;DR

This paper introduces a computationally efficient method for simulating self-gravity in large-scale hydrodynamical models by transforming the Poisson equation into an inhomogeneous wave equation, compatible with advanced computational techniques.

Contribution

The paper presents a novel approach that simplifies self-gravity calculations, reducing computational time and enabling compatibility with parallel and adaptive mesh methods.

Findings

Results agree with traditional Poisson solutions when domain size is large or boundary conditions are appropriate.

Method significantly reduces computational time compared to existing techniques.

Compatible with parallel computation, nested grids, and adaptive mesh refinement.

Abstract

A new computationally efficient method has been introduced to treat self-gravity in mesh based hydrodynamical simulations. It is applied simply by slightly modifying the Poisson equation into an inhomogeneous wave equation. This roughly corresponds to the weak field limit of the Einstein equations in general relativity, and as long as the gravitation propagation speed is taken to be larger than the hydrodynamical characteristic speed, the results agree with solutions for the Poisson equation. The solutions almost perfectly agree if the domain is taken large enough, or appropriate boundary conditions are given. Our new method can not only significantly reduce the computational time compared with existent methods, but is also fully compatible with massive parallel computation, nested grids and adaptive mesh refinement techniques, all of which can accelerate the progress in computational astrophysics and cosmology.