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Boundary conditions (BCs) play an essential role in lattice Boltzmann (LB) simulations. This paper investigates several most commonly applied BCs by evaluating the relative L2-norm errors of the LB simulations for two-dimensional (2-D) Poiseuille flow. It is found that the relative L2-norm error resulting from FHML's BC is smaller than that from other BCs as a whole. Then, based on the FHML's BC, it formulates an LB model for simulating fluid flows in 2-D channel with complex geometries. Afterwards, the flows between two inclined plates, in a pulmonary blood vessel and in a blood vessel with local expansion region, are simulated. The numerical results are in good agreement with the analytical predictions and clearly show that the model is effective. It is expected that the model can be extended to simulate some real biologic flows, such as blood flows in arteries, vessels with stenosises, aneurysms and bifurcations, etc.

A biconcave particle suspended in a Poiseuille flow is investigated by the multiple-relaxation-time lattice Boltzmann method with the Galilean-invariant momentum exchange method. The lateral migration and equilibrium of the particle are similar to the Segre-Silberberg effect in our numerical simulations. Surprisingly, two lateral equilibrium positions are observed corresponding to the releasing positions of the biconcave particle. The upper equilibrium positions significantly decrease with the increasing Reynolds number, whereas the lower ones are almost insensitive to the Reynolds number. Interestingly, the regular wave accompanied by nonuniform rotation is exhibited in the lateral movement of the biconcave particle. It can be attributed to the fact that the biconcave shape in various postures interacts with the parabolic velocity distribution of the Poiseuille flow. A set of contours illustrate the dynamic flow field when the biconcave particle has successive postures in a rotating period.