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Fluctuating multicomponent lattice Boltzmann model.

D Belardinelli1, M Sbragaglia1, L Biferale1

  • 1Department of Physics, University of Rome "Tor Vergata," Via della Ricerca Scientifica 1, 00133 Rome, Italy.

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This study extends fluctuating lattice Boltzmann equations (FLBEs) to multicomponent fluids, incorporating thermal fluctuations. The new model accurately describes ideal and nonideal fluid behaviors with mean-field interactions.

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Area of Science:

  • Computational fluid dynamics
  • Statistical mechanics
  • Kinetic theory

Background:

  • Current fluctuating lattice Boltzmann equations (FLBEs) are limited to single-component fluids.
  • Modeling multicomponent fluid dynamics requires incorporating thermal fluctuations at a fundamental level.

Purpose of the Study:

  • To extend the fluctuating Boltzmann equation to multicomponent fluid systems.
  • To incorporate thermal fluctuations into a kinetic theory framework for multicomponent fluids.
  • To develop a computational model for simulating fluctuating multicomponent fluid dynamics.

Main Methods:

  • Linearization of the fluctuating Boltzmann equation to apply linear fluctuation theory.
  • Derivation of noise covariances using the fluctuation-dissipation theorem at the kinetic level.
  • Projection of the Boltzmann equation onto an orthonormal Hermite basis.
  • Integration of the fluctuating Boltzmann equation with discrete velocities to obtain FLBEs for multicomponent fluids.

Main Results:

  • The developed model successfully incorporates thermal fluctuations into multicomponent fluid dynamics.
  • Expressions for noise covariances were derived directly from kinetic theory.
  • The method is applicable to both ideal and nonideal multicomponent fluids.
  • Numerical simulations with lattice-based mean-field interactions demonstrated proper system thermalization.

Conclusions:

  • The extended fluctuating Boltzmann equation provides a robust framework for simulating fluctuating multicomponent fluids.
  • This work bridges the gap between kinetic theory and computational fluid dynamics for complex fluid systems.
  • The model offers a foundation for future research in areas like phase transitions and turbulence in multicomponent systems.