Semi-implicit-linearized multiple-relaxation-time formulation of lattice Boltzmann schemes for mixture modeling

Area of Science:

• Computational fluid dynamics
• Multiphase flow modeling

Background:

• Existing lattice Boltzmann models for mixtures have limitations in independently controlling transport properties.
• The Hamel model provides a general framework for deriving various lattice Boltzmann models.

Purpose of the Study:

• To develop a multiple-relaxation-time (MRT) lattice Boltzmann model for mixture simulations based on the Hamel model.
• To enable independent tuning of species diffusivity, mixture kinematic viscosity, and mixture bulk viscosity.
• To model pressure-driven diffusion effectively, especially for disparate mass ratios.

Main Methods:

• Application of the multiple-relaxation-time (MRT) approach to the Hamel model.
• Imposing physical constraints to reduce the MRT Hamel model to a generalized MRT lattice-Boltzmann Gross-Krook model.
• Development of a semi-implicit-linearized backward Euler numerical scheme for stability and efficiency.
• Utilizing asymptotic analysis in the low-Mach-number limit.

Main Results:

• The developed model allows independent control over key mixture transport properties.
• The numerical scheme enhances stability and reduces computational demand, suitable for parallel implementations.
• The model is consistent with Fick and Maxwell-Stefan models in the macroscopic limit.

Conclusions:

• The proposed MRT lattice Boltzmann model offers a flexible and efficient framework for mixture simulations.
• The numerical approach provides a stable and computationally advantageous solution for complex fluid dynamics problems.
• The model's consistency with established diffusion models validates its applicability.