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Modeling and simulation of multiphase flows in complex geomerties arechallenging due to the complexity in describing the interface topology changesamong different phases and the difficulty in implementing the boundaryconditions on the irregular solid surface. In this work, we first developed adiffuse-domain (DD) based phase-field model for multiphase flows in complexgeometries. In this model, the irregular fluid region is embedded into a largerand regular domain by introducing a smooth characteristic function. Then, thereduction-consistent and conservative phase-field equation for the multiphasefield and the consistent and conservative Navier-Stokes equations for the flowfield are reformulated as the diffuse-domain based consistent and conservative(DD-CC) equations where some additional source terms are added to reflect theeffects of boundary conditions. In this case, there is no need to directlytreat the complex boundary conditions on the irregular solid surface, andadditionally, based on a matched asymptotic analysis, it is also shown that theDD-CC equations can converge to the original governing equations as theinterface width parameter tends to zero. Furthermore, to solve the DD-CCequations, we proposed a novel and simple lattice Boltzmann (LB) method with aHermite-moment-based collision matrix which can not only keep consistent andconservation properties, but also improve the numerical stability with aflexible parameter. With the help of the direct Taylor expansion, themacroscopic DD-CC equations can be recovered correctly from the present LBmethod. Finally, to test the capacity of LB method, several benchmarks andcomplex problems are considered, and the numerical results show that thepresent LB method is accurate and efficient for the multiphase flows in complexgeomerties.

A consistent and conservative diffuse-domain lattice Boltzmann method for multiphase flows in complex geometries