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Modified phase-field-based lattice Boltzmann model for incompressible multiphase flows.

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A new multiple-relaxation-time (MRT) lattice Boltzmann model accurately simulates immiscible multiphase fluids. This improved model avoids artificial terms, enhancing stability and reducing numerical errors in fluid dynamics simulations.

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Area of Science:

  • Computational fluid dynamics
  • Multiphase flow modeling
  • Phase-field theory

Background:

  • Accurate simulation of immiscible multiphase fluids is crucial in many scientific and engineering fields.
  • Existing lattice Boltzmann models often introduce artificial terms that can lead to instabilities.
  • The phase-field theory provides a robust framework for capturing complex interface dynamics.

Purpose of the Study:

  • To develop a novel multiple-relaxation-time (MRT) lattice Boltzmann model for immiscible multiphase fluids.
  • To eliminate artificial terms in the phase-field equation for improved accuracy and stability.
  • To validate the model's performance through benchmark multiphase flow simulations.

Main Methods:

  • Implementation of a modified MRT lattice Boltzmann model using the Allen-Cahn equation for interface tracking.
  • Adoption of an off-diagonal relaxation matrix to ensure exact recovery of the phase-field equation.
  • Coupling interface dynamics with hydrodynamic properties using a pressure-evolution lattice Boltzmann equation.
  • Conducting benchmark simulations: static drop, Rayleigh-Taylor instability, and rising bubble.

Main Results:

  • The modified MRT model successfully recovers the target phase-field equation without artificial terms.
  • Comparative studies revealed that artificial terms cause unphysical diffusion and instability at higher March numbers.
  • The proposed model demonstrates superior accuracy in reducing numerical errors by adjusting free parameters.
  • Simulations of rising bubbles at high density ratios show excellent agreement with FEM-based level set and phase-field models.

Conclusions:

  • The developed MRT lattice Boltzmann model offers a stable and accurate approach for simulating immiscible multiphase flows.
  • Eliminating artificial terms is essential for preventing unphysical behaviors, especially at higher flow regimes.
  • The model's validity is confirmed through successful benchmark case simulations, highlighting its potential for complex fluid dynamics problems.