Direct simulation Monte Carlo

Thermodynamic equilibrium

Mathematics

Mechanics

Lattice Boltzmann methods

Monte Carlo method

Classical mechanics

Thermodynamics

Spurious relationship

Statistical physics

Turbulence

Discretization

Dynamic Monte Carlo method

Boltzmann equation

Work (physics)

HPP model

Boltzmann relation

Equation of state

Statistics

Mathematical analysis

Bhatnagar–Gross–Krook operator

Physics

Reynolds number

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