A Lattice Boltzmann method for two-phase flows on adaptive Cartesian grids*

We present a numerical scheme, which is capable of predicting liquid-gas multiphase flows on adaptive Cartesian grids. Each of the two fluid phases is modeled by a separate solver using a Lattice Boltzmann Method (LBM) such that density and viscosity can be controlled independently, and high density and viscosity ratios can be achieved. To capture the motion of the liquid-gas interface, a level-set method is used, which is advected by the local fluid velocity. It is used to impose the boundary conditions in the phase boundary cells by evaluating the boundary normal and curvature, e.g., for the determination of the surface tension. The stress tensor on both sides of the interface is evaluated to obtain a correction term for the bounce back boundary condition such that the kinematic coupling condition and the jump condition for the pressure is fulfilled. All solvers, i.e., the LBM solvers for the liquid and gas phase, and the level set solver, operate on a joint hierarchical Cartesian grid, which facilitates an efficient parallelization and enables adaptive mesh refinement with a dynamic load balancing. The presented method is validated by generic test cases for two-phase bubble flows. Details of the numerical method, results of the validation, and its application to the analysis of multiphase flow problems will be presented.