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Multiscale temporal integrators for fluctuating hydrodynamics.

Steven Delong1, Yifei Sun1, Boyce E Griffith2

  • 1Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 24, 2015
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Summary
This summary is machine-generated.

New temporal integrators accurately solve Langevin stochastic differential equations for fluctuating hydrodynamics. These methods maintain second-order weak accuracy, enabling study of giant nonequilibrium concentration fluctuations in fluids.

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Area of Science:

  • Computational physics
  • Fluid dynamics
  • Numerical analysis

Background:

  • Fluctuating hydrodynamics describes fluid systems with inherent random fluctuations.
  • Solving Langevin stochastic differential equations (SDEs) is crucial for modeling these systems.
  • Previous work established a foundation for developing accurate numerical methods.

Purpose of the Study:

  • To develop novel temporal integrators for Langevin SDEs in fluctuating hydrodynamics.
  • To ensure these integrators maintain second-order weak accuracy for linearized systems.
  • To extend methods for overdamped limits with fast and slow variables.

Main Methods:

  • Developed predictor-corrector schemes by adding fluctuations to deterministic solvers.
  • Constructed general schemes, recommending explicit midpoint and implicit trapezoidal methods.
  • Proposed random finite differences for stochastic drift terms in limiting dynamics.

Main Results:

  • Demonstrated second-order weak accuracy for linearized fluctuating hydrodynamics.
  • Successfully applied integrators to study giant nonequilibrium concentration fluctuations.
  • Investigated effects of gravity and fluid inertia on concentration fluctuations.

Conclusions:

  • The developed temporal integrators offer accurate solutions for Langevin SDEs in fluctuating hydrodynamics.
  • These methods are effective for simulating nonequilibrium phenomena like giant concentration fluctuations.
  • Including gravity and fluid inertia is essential for accurate modeling at small wave numbers.