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Consistent lattice Boltzmann equations for phase transitions.

D N Siebert1, P C Philippi2, K K Mattila2

  • 1Federal University of Santa Catarina, 89218-000 Joinville, SC, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 11, 2014
PubMed
Summary
This summary is machine-generated.

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A novel athermal lattice Boltzmann scheme (LBM) simulates fluid phase transitions by incorporating source terms into kinetic equations. This method accurately models interface dynamics and thermodynamic properties for various equations of state.

Area of Science:

  • Computational physics
  • Fluid dynamics
  • Thermodynamics

Background:

  • Conventional computational fluid dynamics (CFD) methods struggle with mesoscopic fluid behavior.
  • Lattice Boltzmann Method (LBM) offers an alternative by modeling fluids based on discrete kinetic equations.
  • Phase transitions and interface dynamics require specialized approaches within LBM.

Purpose of the Study:

  • To propose a novel athermal lattice Boltzmann scheme for simulating fluid phase transitions.
  • To ensure consistency between the kinetic model and diffuse interface models.
  • To analytically derive key interface properties and numerically validate the scheme.

Main Methods:

  • Developed a continuous kinetic model from the Liouville equation using mean-field interactions.

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  • Ensured consistency with diffuse interface models via Helmholtz free energy.
  • Discretized the kinetic equation using a quadrature method and a third-order scheme for the streaming term.
  • Approximated spatial derivatives in source terms with high-order schemes.
  • Validated numerically by measuring speed of sound and retrieving coexistence curves.

    • Main Results:

    • Analytically derived density profiles, interface thickness, and surface tension for a liquid-vapor interface.
    • Demonstrated consistency with diffuse interface models.
    • Successfully retrieved coexistence curves and interface density profiles.
    • Investigated spurious currents near the interface.
    • Simulations covered multiple equations of state (Van der Waals, Redlich-Kwong, etc.).

    Conclusions:

    • The proposed athermal LBM scheme is effective for simulating phase transitions.
    • The method accurately captures interface phenomena and thermodynamic properties.
    • The scheme provides a robust framework for studying fluid behavior across different equations of state.