Reduction of the spurious currents in the multiphase lattice Boltzmann method

Recently, the lattice Boltzmann method(LBM) has gained much attention for its ability to simulate fluid flows, and for its potential advantages over a conventional CFD method. The key advantages of LBM are, (1) suitability for parallel computations, (2) absence of the need to solve the time-consuming Poisson equation for a pressure, and (3) an ease with multiphase flows, complex geometries and interfacial dynamics may be treated. A phenomenon known as spurious currents was first discovered in an early LB multiphase model as a small but finite amplitude circulating flow near the interface of a stationary bubble. The flow pattern was found to possess the same symmetry as the underlying lattice and the magnitude of the velocity scales with the surface tension and the inversion of the viscosity. Similar flow patterns have been found in the subsequent VOF, level set models for a multiphase flow although both the magnitude and the spatial extent of the spurious current are much reduced. The presence of the anomalous circulation has caused some skepticism about the applicability of the LB method for the simulation of a multiphase flow. For engineering applications, the small velocities also compromise the accuracy of the numerical results, especially in situations where the detailed dynamics of the interface is of critical importance. Several attempts have been made to understand the origin and to reduce the magnitude of the spurious velocities. Shan showed that the origin of the spurious currents in the non-ideal gas LB model could be understood as caused by the lack of a sufficient isotropy when the gradient of the density is calculated. Lee et al. concluded that discretization errors in the computation of the intermolecular force cause spurious currents. They showed that these currents can be eliminated if the potential form of the intermolecular force is used with a compact isotropic discretization. In the present work, the lattice Boltzmann model for multiphase flows proposed by Zheng et al. is used for simulating a stationary droplet in a quiescent environment. By adopting a finite difference gradient operator of a sufficient isotropy, the spurious currents can be made to be small. The main objective of the present work is to establish the lattice Boltzmann method as a viable tool for the simulation of multiphase or multi-component flows