Projection Method for the Fluctuating Hydrodynamics Equations

TL;DR

This paper introduces a novel projection-based numerical method for solving incompressible fluctuating hydrodynamics equations, effectively capturing thermal fluctuations at small scales and addressing boundary condition challenges.

Contribution

The paper presents a new projection method for FHD equations that analyzes and reduces splitting errors, improving accuracy in non-periodic boundary conditions.

Findings

Successfully reproduces stochastic fluid properties at small scales

Reduces splitting errors with iterative corrections

Demonstrates potential for multi-physics simulations

Abstract

Computational fluctuating hydrodynamics aims at understanding the impact of thermal fluctuations on fluid motions at small scales through numerical exploration. These fluctuations are modeled as stochastic flux terms and incorporated into the classical Navier-Stokes equations, which need to be solved numerically. In this paper, we present a novel projection-based method for solving the incompressible fluctuating hydrodynamics (FHD) equations. By analyzing the equilibrium structure factor spectrum of the velocity field for the linearized FHD equations, we investigate how the inherent splitting errors affect the numerical solution of the stochastic partial differential equations in the presence of non-periodic boundary conditions, and how iterative corrections can reduce these errors. Our computational examples demonstrate both the capability of our approach to reproduce correctly stochastic properties of fluids at small scales as well as its potential use in the simulations of multi-physics problems.