An Introduction to Computational Fluctuating Hydrodynamics

TL;DR

This paper introduces fluctuating hydrodynamics and discusses finite volume numerical schemes for stochastic PDEs, emphasizing their application in modeling mesoscopic fluid dynamics with thermal fluctuations, and provides a Python demonstration program.

Contribution

It presents an accessible introduction to computational fluctuating hydrodynamics and details finite volume schemes, including a practical Python implementation.

Findings

Finite volume schemes effectively model stochastic hydrodynamics.

The Python program demonstrates practical implementation.

FHD captures thermal fluctuations in mesoscopic fluids.

Abstract

These notes are an introduction to fluctuating hydrodynamics (FHD) and the formulation of numerical schemes for the resulting stochastic partial differential equations (PDEs). Fluctuating hydrodynamics was originally introduced by Landau and Lifshitz as a way to put thermal fluctuations into a continuum framework by including a stochastic forcing to each dissipative transport process (e.g., heat flux). While FHD has been useful in modeling transport and fluid dynamics at the mesoscopic scale, theoretical calculations have been feasible only with simplifying assumptions. As such there is great interest in numerical schemes for Computational Fluctuating Hydrodynamics (CFHD). There are a variety of algorithms (e.g., spectral, finite element, lattice Boltzmann) but in this introduction we focus on finite volume schemes. Accompanying these notes is a demonstration program in Python available on GitHub (https://github.com/AlejGarcia/IntroFHD).