Axisymmetric phase-field-based lattice Boltzmann model with reduced spurious velocity for incompressible two-phase flows

Abstract

In this work, a phase-field-based lattice Boltzmann method with reduced spurious velocity is developed for axisymmetric incompressible two-phase flows. Two sets of lattice Boltzmann equations with multiple-relaxation-time collision operators are used to, respectively, recover the conservative Allen–Cahn equation for interface capturing and the hydrodynamic equations. To reduce the spurious velocity, a novel correction term is introduced into the hydrodynamic lattice Boltzmann equation so that the leading truncation error related to the third derivatives of pressure can be partially removed. Simultaneously, the radius-weighted mirror symmetric boundary is applied to the axis of symmetry because all the moments of the distribution functions are proportional to the radial coordinate. Furthermore, the bulk viscosity is able to be changed independent of the shear viscosity through redefining the source term. A series of classical numerical experiments, including stationary droplet, oscillation of an elliptical droplet, bubble rising, drop splashing, have been conducted to test the performance of the proposed model. Numerical results agree well with the analytical solution and published data in literature, which demonstrates the improved accuracy and numerical stability.