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Spurious velocities arising from the imperfect offset of the undesired termat the discrete level are frequently observed in numerical simulations ofequilibrium multiphase flow systems using the lattice Boltzmann equation (LBE)method. To capture the physical equilibrium state of two-phase fluid systemsand eliminate spurious velocities, a well-balanced LBE model based on theincompressible phase-field theory is developed. In this model, the equilibriumdistribution function for the Cahn-Hilliard (CH) equation is designed bytreating the convection term as a source to avoid the introduction of undesiredterms, enabling achievement of possible discrete force balance. Furthermore,this approach allows for the attainment of a divergence-free velocity field,effectively mitigating the impact of artificial compression effects andenhancing numerical stability. Numerical tests, including a flat interfaceproblem, a stationary droplet, and the coalescence of two droplets, demonstratethe well-balanced properties and improvements in the stability of the presentmodel.

A well-balanced lattice Boltzmann model for binary fluids based on the incompressible phase-field theory