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An Introduction to Computational Fluctuating Hydrodynamics

Year: 2024

Type: preprint

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).

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2406.12157

Authors: Garcia, Alejandro L., Bell, John B., Nonaka, Andrew, Srivastava, Ishan, Ladiges, Daniel, Kim, Changho

Institutions: San Jose State University, Lawrence Berkeley National Laboratory, University of California, Merced

Language: English

Topic: Lattice Boltzmann Simulation Studies

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research

Awards: G1286236842, G1799333409, G3083819904, G419881185, G42916606, G4501827968, G498139845, G969889393

OpenAlex ID: W4399836903

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Cited by: 1

Related to: 10