Bhatnagar–Gross–Krook operator

Statistics

Boltzmann relation

Physics

Statistical physics

Dynamic Monte Carlo method

Thermodynamic equilibrium

Mathematical analysis

Direct simulation Monte Carlo

Boltzmann equation

Reynolds number

Work (physics)

Monte Carlo method

Turbulence

Lattice Boltzmann methods

Mathematics

Mechanics

HPP model

Discretization

Classical mechanics

Spurious relationship

Thermodynamics

Physics of Fluids

The standard lattice Boltzmann equation (LBE) method usually fails to capture the physical equilibrium state of a two-phase fluid system, i.e., zero velocity and constant chemical potential. Consequently, spurious velocities and inconsistent thermodynamic density properties are frequently encountered in LBE simulations. In this work, based on a rigorous analysis of the discrete balance equation of LBE, we identify the structure of the force imbalance due to discretization errors from different parts. Then a well-balanced LBE is proposed which can achieve the discrete equilibrium state. The well-balanced properties of the LBE are confirmed by some numerical tests of a flat interface problem and a droplet system.

Well-balanced lattice Boltzmann model for two-phase systems