Hydrodynamic force evaluation in lattice Boltzmann method

The lattice Boltzmann method is a mesoscopic numerical method originating from kinetic theory and the cellular automaton concept. It has been successfully used to simulate complex flows, especially particle suspensions and multiphase flows. In this paper, we review our recent work on fluid-structure interactions and nonideal force evaluations. We introduced the relative velocity into the treatment of fluid-structure interfacial dynamics and proposed a Galilean invariant momentum exchange method. The method is simple, accurate and efficient. It is independent of boundary geometries and only uses the local data, thus it is convenient to implement parallelization and 3D simulations. The numerical simulations are so vastly improved that the force fluctuations are very small and a time average procedure becomes unnecessary. To simulate phase separation and two-phase flow, we directly evaluated the nonideal force based on the free energy and proposed a multiphase flow model. Thermodynamic consistency and Galilean invariance of the model are theoretically satisfied and numerically verified. This model can be easily implemented and cooperated with various equations of state to simulate all kinds of the multiphase systems. Chemical potential is an effective way to drive phase transition or express surface wettability. In the further study, we proposed another multiphase flow model based on chemical potential. It is mathematically equivalent to the previous one, but is more computationally efficient owing to avoiding the calculations of pressure tensor and tensor divergence. Together with the chemical potential boundary condition, the model can effectively simulate wetting phenomena. The numerical results show that the contact angle can be linearly tuned by the surface chemical potential.