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Article
Low Mach Number Fluctuating Hydrodynamics of Diffusively Mixing Fluids
Communications in Applied Mathematics and Computational Science (2014)
  • Aleksandar Donev, New York University
  • Andy J Nonaka, Lawrence Berkeley National Laboratory
  • Yifei Sun, Leon H. Charney Division of Cardiology
  • Thomas Fai, New York University
  • Alejandro Garcia, San Jose State University
  • John B Bell, Lawrence Berkeley National Laboratory
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 eliminate the fast isentropic 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 spatio-temporal 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. We construct several explicit Runge-Kutta temporal integrators that strictly maintain the equation of state constraint. The resulting spatio-temporal 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 simplications neglecting the spatial non-homogeneity 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.
Keywords
  • fluctuating hydrodynamics,
  • low Mach expansion,
  • molecular dynamics,
  • giant fluctuations
Publication Date
2014
DOI
10.2140/camcos.2014.9.47
Publisher Statement
Citation Information
Aleksandar Donev, Andy J Nonaka, Yifei Sun, Thomas Fai, et al.. "Low Mach Number Fluctuating Hydrodynamics of Diffusively Mixing Fluids" Communications in Applied Mathematics and Computational Science Vol. 9 Iss. 1 (2014) p. 47 - 105 ISSN: 1559-3940
Available at: http://works.bepress.com/alejandro_garcia1/1/