Multiscale temporal integrators for fluctuating hydrodynamics

Steven Delong, Yifei Sun, Boyce E. Griffith, Eric Vanden Eijnden, Aleksandar Donev

Research output: Contribution to journalArticle

Abstract

Following on our previous work [S. Delong, B. E. Griffith, E. Vanden-Eijnden, and A. Donev, Phys. Rev. E 87, 033302 (2013)PLEEE81539-375510.1103/PhysRevE.87.033302], we develop temporal integrators for solving Langevin stochastic differential equations that arise in fluctuating hydrodynamics. Our simple predictor-corrector schemes add fluctuations to standard second-order deterministic solvers in a way that maintains second-order weak accuracy for linearized fluctuating hydrodynamics. We construct a general class of schemes and recommend two specific schemes: an explicit midpoint method and an implicit trapezoidal method. We also construct predictor-corrector methods for integrating the overdamped limit of systems of equations with a fast and slow variable in the limit of infinite separation of the fast and slow time scales. We propose using random finite differences to approximate some of the stochastic drift terms that arise because of the kinetic multiplicative noise in the limiting dynamics. We illustrate our integrators on two applications involving the development of giant nonequilibrium concentration fluctuations in diffusively mixing fluids. We first study the development of giant fluctuations in recent experiments performed in microgravity using an overdamped integrator. We then include the effects of gravity and find that we also need to include the effects of fluid inertia, which affects the dynamics of the concentration fluctuations greatly at small wave numbers.

Original languageEnglish (US)
Article number063312
JournalPhysical Review E
Volume90
Issue number6
DOIs
StatePublished - Dec 18 2014

Fingerprint

Fluctuating Hydrodynamics
integrators
hydrodynamics
Fluctuations
predictor-corrector methods
Fluid
Predictor-corrector Methods
Microgravity
Predictor-corrector
Midpoint
Multiplicative Noise
fluids
microgravity
inertia
Inertia
Non-equilibrium
System of equations
Stochastic Equations
Finite Difference
Gravity

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Multiscale temporal integrators for fluctuating hydrodynamics. / Delong, Steven; Sun, Yifei; Griffith, Boyce E.; Vanden Eijnden, Eric; Donev, Aleksandar.

In: Physical Review E, Vol. 90, No. 6, 063312, 18.12.2014.

Research output: Contribution to journalArticle

Delong, Steven ; Sun, Yifei ; Griffith, Boyce E. ; Vanden Eijnden, Eric ; Donev, Aleksandar. / Multiscale temporal integrators for fluctuating hydrodynamics. In: Physical Review E. 2014 ; Vol. 90, No. 6.
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