Modified radius-weighted lattice Boltzmann model to address singularities in axisymmetric multiphase flows

The radius-weighted lattice Boltzmann model has achieved great success in the simulation of axisymmetric flows. However, severe spurious currents near the axis are observed when this model is extended to simulate axisymmetric multiphase flows. In this study, to determine the origin of this singularity, we conducted a truncation error analysis based on high-order Taylor series expansion and identified the leading error terms through dimensionless analysis. By neglecting the error terms in proportion to the radius, we obtained the final forms of the singular terms in the axisymmetric lattice Boltzmann model. We proposed a modified model by including an additional correction term, to remove the singularity at the third order. We validated the proposed model using numerical tests for flat and spherical interfaces. Results showed that the present modified model reduced the spurious currents near the axis by two orders of magnitude compared with the original model. This modified model also has been successfully applied to predict bubble dynamics in an air-water system. Our numerical results are in excellent agreement with available experimental observations in terms of bubble shapes and terminal velocities.