Low mach number fluctuating hydrodynamics of diffusively mixing fluids

Aleksandar Donev, Andy Nonaka, Yifei Sun, Thomas G. Fai, Alejandro L. Garcia, John B. Bell

Research output: Contribution to journalArticle

Abstract

We formulate low Mach number fluctuating hydrodynamic equations appropriate for modeling diffusive mixing in isothermal mixtures of fluids with different density and transport coefficients. These equations represent a coarse-graining of the microscopic dynamics of the fluid molecules in both space and time and eliminate the fluctuations in pressure associated with the propagation of sound waves by replacing the equation of state with a local thermodynamic constraint. We demonstrate that the low Mach number model preserves the spatiotemporal spectrum of the slower diffusive fluctuations. We develop a strictly conservative finite-volume spatial discretization of the low Mach number fluctuating equations in both two and three dimensions and construct several explicit Runge-Kutta temporal integrators that strictly maintain the equation-of-state constraint. The resulting spatiotemporal discretization is second-order accurate deterministically and maintains fluctuation-dissipation balance in the linearized stochastic equations. We apply our algorithms to model the development of giant concentration fluctuations in the presence of concentration gradients and investigate the validity of common simplifications such as neglecting the spatial nonhomogeneity of density and transport properties. We perform simulations of diffusive mixing of two fluids of different densities in two dimensions and compare the results of low Mach number continuum simulations to hard-disk molecular-dynamics simulations. Excellent agreement is observed between the particle and continuum simulations of giant fluctuations during time-dependent diffusive mixing.

Original languageEnglish (US)
Pages (from-to)47-105
Number of pages59
JournalCommunications in Applied Mathematics and Computational Science
Volume9
Issue number1
DOIs
StatePublished - 2014

Fingerprint

Fluctuating Hydrodynamics
Low Mach number
Mach number
Hydrodynamics
Fluctuations
Fluid
Fluids
Equations of state
Equation of State
Two Dimensions
Continuum
Strictly
Discretization
Hard disk storage
Simulation
Coarse-graining
Transport properties
Hydrodynamic Equations
Transport Coefficients
State Constraints

Keywords

  • Fluctuating hydrodynamics
  • Giant fluctuations
  • Low mach expansion
  • Molecular dynamics

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Theory and Mathematics
  • Computer Science Applications

Cite this

Low mach number fluctuating hydrodynamics of diffusively mixing fluids. / Donev, Aleksandar; Nonaka, Andy; Sun, Yifei; Fai, Thomas G.; Garcia, Alejandro L.; Bell, John B.

In: Communications in Applied Mathematics and Computational Science, Vol. 9, No. 1, 2014, p. 47-105.

Research output: Contribution to journalArticle

Donev, Aleksandar ; Nonaka, Andy ; Sun, Yifei ; Fai, Thomas G. ; Garcia, Alejandro L. ; Bell, John B. / Low mach number fluctuating hydrodynamics of diffusively mixing fluids. In: Communications in Applied Mathematics and Computational Science. 2014 ; Vol. 9, No. 1. pp. 47-105.
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