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In this paper, a fractional step lattice Boltzmann method is proposed tomodel two-phase flows with large density differences by solving Cahn-Hilliardphase-field equation and the incompressible Navier-Stokes equations.In order tomaintain a hyperbolic tangent property of the interface profile and conservethe volume, an interfacial profile correction term and a flux correction termare added into the original Cahn-Hilliard equation respectively. By using afractional step scheme, the modified Cahn-Hilliard equation is split into twosub-equations. One is solved in the framework of lattice Boltzmann equationmethod. The other is solved by the finite difference method. Compared with theprevious lattice Boltzmann methods, the proposed method is able to maintain theorder parameter within a physically meaningful range, which is conductive totrack the interface accurately. In addition, the multi-relaxation-timecollision model and a high-order compact selective filter operation areemployed to enhance the numerical stability. The proposed method can simulatetwo-phase fluid flows with the density ratio up to $1000$. In order to validatethe accuracy and capability of the method, several benchmark problems,including single vortex deform of a circle, translation of a drop,Laplace-Young law, capillary wave and rising bubble with large density ratios,are presented. The results are in good agreement with the analytical solutionsand the data in the literature for the investigated benchmarks.

A fractional step lattice Boltzmann model for two phase flows with large density differences