Numerical simulations of non-relativistic stochastic fluids via the Metropolis algorithm

TL;DR

This paper introduces a Metropolis algorithm-based numerical method for simulating non-relativistic stochastic fluids in two dimensions, effectively handling fluctuations and dissipation in hydrodynamic equations.

Contribution

The authors develop a versatile Metropolis algorithm for simulating stochastic hydrodynamics, capable of incorporating fluctuations and dissipation simultaneously in non-relativistic fluids.

Findings

Successfully implemented the algorithm in test cases

Demonstrated renormalization of shear viscosity through simulations

Algorithm adaptable to other hydrodynamic theories

Abstract

Stochastic hydrodynamics provides a dynamical framework for the evolution of fluctuations in heavy-ion collisions, but poses significant challenges in numerical simulations. We present an algorithm for the simulation of non-relativistic stochastic fluids in two spatial dimensions in a box. We use the robust Metropolis algorithm, handling fluctuations and dissipation at once by systematically replacing dissipative terms in the hydrodynamic equations by random forces. The algorithm can easily be modified for numerical simulations of other hydrodynamic theories. We present test cases as well as numerical calculations of the renormalization of shear viscosity.