Reduction of spurious velocity in the free-energy-based lattice Boltzmann method for large density ratio

Abstract

The spurious velocity around curved interface, arising from the calculation of the Poisson equation with staggered grids, is reduced in the free-energy-based two-phase flow lattice Boltzmann method (LBM) for large density ratios. It is found that the pressure calculation from the Poisson equation, using the successive over-relaxation method with staggered grids, would introduce anisotropic discretization errors and lead to deviations of its calculated value from the theoretical prediction. Moreover, the anisotropic pressure would induce a large magnitude of spurious velocity, which is the driving force for droplet shape deformation. By blending the velocity components in the discretization equations of the Poission equation from two types of staggered grids that separately make use of the velocity components in the orthogonal and the diagonal directions, the magnitude of the spurious velocity and the droplet deformation are diminshed. It is found that, by appropriate choice of the blending factor, the magnitude of the spurious velocity can be reduced to half of its original value, and the shape deformation and pressure deviation from the theoretical prediction can be minimized.

Keywords

• spurious velocity
• anisotropic error
• poisson equation
• lattice boltzmann method
• water droplet
• shape deformation
• free energy
• successive over-relaxation