Efficient computations for high density ratio rising bubble flows using a diffused interface, coupled lattice Boltzmann-level set scheme

A mass conserving, diffused interface, coupled Lattice Boltzmann-level set scheme is proposed and numerically studied for the simulation of high density and viscosity ratio multiphase flows. The approach is based on the pressure evolution formulation of the lattice Boltzmann equation, which is then coupled with the level set equation to capture a diffused level set function. Multiple relaxation time collision and isotropic force discretization techniques are employed to further reinforce the stability and accuracy of the LBM solver and a monolithic approach is employed to convect the level set function with minimal computations to preserve a smooth density profile. We present extensive investigations for numerical accuracy through performing benchmark simulations for rising bubble problems. It is observed that the proposed scheme is successful in producing accurate results as compared to those from high precision 2D finite element solutions in Hysing et al. (2009), offering a remarkable improvement in mass conservation and characteristic benchmark quantities upon our previous sharp interface coupled model described in Safi and Turek (2014). Moreover, parallel scalability of the coupled LB scheme is shown to be preserved through performing efficient CPU- and GPGPU-based computations.