Towards a consistent lattice Boltzmann model for two-phase fluids

We revisit the construction of discrete kinetic models for single-component isothermal two-phase flows. Starting from a kinetic model for a non-ideal fluid, we show that, under conventional scaling, the Navier–Stokes equations with a non-ideal equation of state are recovered in the hydrodynamic limi...

Full description

Saved in:
Bibliographic Details
Published in:Journal of fluid mechanics 2022-12, Vol.953, Article A4
Main Authors: Hosseini, S.A., Dorschner, B., Karlin, I.V.
Format: Article
Language:English
Subjects:
Benchmarks
Coalescence
Consistency
Dimensions
Dynamic tests
Energy
Engines
Equations of state
Flow velocity
Fluid flow
Fluids
Hydrodynamics
Ideal fluids
Interfaces
JFM Papers
Lagrange multiplier
Lattice vibration
Mathematical models
Mercury
Navier-Stokes equations
Ratios
Scaling
Simulation
Sound velocity
Surface tension
Thermal properties
Thermodynamic properties
Thermodynamics
Two phase flow
Viscosity
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We revisit the construction of discrete kinetic models for single-component isothermal two-phase flows. Starting from a kinetic model for a non-ideal fluid, we show that, under conventional scaling, the Navier–Stokes equations with a non-ideal equation of state are recovered in the hydrodynamic limit. A scaling based on the smallness of velocity increments is then introduced, which recovers the full Navier–Stokes–Korteweg equations. The proposed model is realized on a standard lattice and validated on a variety of benchmarks. Through a detailed study of thermodynamic properties including co-existence densities, surface tension, Tolman length and sound speed, we show thermodynamic consistency, well-posedness and convergence of the proposed model. Furthermore, hydrodynamic consistency is demonstrated by verification of Galilean invariance of the dissipation rate of shear and normal modes and the study of visco-capillary coupling effects. Finally, the model is validated on dynamic test cases in three dimensions with complex geometries and large density ratios such as drop impact on textured surfaces and mercury drops coalescence.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2022.867