Temporal integrators for fluctuating hydrodynamics

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

Research output: Contribution to journalArticle

Abstract

Including the effect of thermal fluctuations in traditional computational fluid dynamics requires developing numerical techniques for solving the stochastic partial differential equations of fluctuating hydrodynamics. These Langevin equations possess a special fluctuation-dissipation structure that needs to be preserved by spatio-temporal discretizations in order for the computed solution to reproduce the correct long-time behavior. In particular, numerical solutions should approximate the Gibbs-Boltzmann equilibrium distribution, and ideally this will hold even for large time step sizes. We describe finite-volume spatial discretizations for the fluctuating Burgers and fluctuating incompressible Navier-Stokes equations that obey a discrete fluctuation-dissipation balance principle just like the continuum equations. We develop implicit-explicit predictor-corrector temporal integrators for the resulting stochastic method-of-lines discretization. These stochastic Runge-Kutta schemes treat diffusion implicitly and advection explicitly, are weakly second-order accurate for additive noise for small time steps, and give a good approximation to the equilibrium distribution even for very strong fluctuations. Numerical results demonstrate that a midpoint predictor-corrector scheme is very robust over a broad range of time step sizes.

Original languageEnglish (US)
Article number033302
JournalPhysical Review E
Volume87
Issue number3
DOIs
StatePublished - Mar 11 2013

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Fluctuating Hydrodynamics
integrators
hydrodynamics
Fluctuations
Predictor-corrector
Equilibrium Distribution
Discretization
Dissipation
dissipation
Runge-Kutta Schemes
Method of Lines
Midpoint
Stochastic Partial Differential Equations
Langevin Equation
Stochastic Methods
Additive Noise
Incompressible Navier-Stokes Equations
Long-time Behavior
Advection
computational fluid dynamics

ASJC Scopus subject areas

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

Cite this

Temporal integrators for fluctuating hydrodynamics. / Delong, Steven; Griffith, Boyce E.; Vanden Eijnden, Eric; Donev, Aleksandar.

In: Physical Review E, Vol. 87, No. 3, 033302, 11.03.2013.

Research output: Contribution to journalArticle

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