Staggered schemes for fluctuating hydrodynamics

Florencio Balboa Usabiaga, John B. Bell, Rafael Delgado-Buscalioni, Aleksandar Donev, Thomas G. Fai, Boyce E. Griffith, Charles S. Peskin

Research output: Contribution to journalArticlepeer-review


We develop numerical schemes for solving the isothermal compressible and incompressible equations of fluctuating hydrodynamics on a grid with staggered momenta. We develop a second-order accurate spatial discretization of the diffusive, advective, and stochastic fluxes that satisfies a discrete fluctuation-dissipation balance and construct temporal discretizations that are at least second-order accurate in time deterministically and in a weak sense. Specifically, the methods reproduce the correct equilibrium covariances of the fluctuating fields to the third (compressible) and second (incompressible) orders in the time step, as we verify numerically. We apply our techniques to model recent experimental measurements of giant fluctuations in diffusively mixing fluids in a microgravity environment [A. Vailati et al., Nat. Comm., 2 (2011), 290]. Numerical results for the static spectrum of nonequilibrium concentration fluctuations are in excellent agreement between the compressible and incompressible simulations and in good agreement with experimental results for all measured wavenumbers.

Original languageEnglish (US)
Pages (from-to)1369-1408
Number of pages40
JournalMultiscale Modeling and Simulation
Issue number4
StatePublished - 2012


  • Fluctuating hydrodynamics
  • Fluctuation-dissipation balance
  • Giant fluctuations
  • Staggered grid

ASJC Scopus subject areas

  • General Chemistry
  • Modeling and Simulation
  • Ecological Modeling
  • General Physics and Astronomy
  • Computer Science Applications


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