UC Davis

We present a sharp-interface method for resolved two-phase incompressible viscous flow based on embedded boundary finite volume discretizations of the individual phase domains. The numerical algorithm is a fractional step method, in which incompressibility is enforced at the half-step and the full-step by solving coupled Hodge projections that respect the jump boundary conditions in pressure and pressure gradient at the interface. Surface tension enters through these boundary conditions. The viscous term in the momentum equations is solved implicitly using a Crank-Nicholson time discretization, respecting the jump conditions on velocity and velocity gradient. The method is implemented with block-structured adaptive mesh refinement. We demonstrate stable behavior in 2D and 3D, with the velocity converging in all norms as measured using Richardson extrapolation. The method successfully models spherical cap bubble shapes and velocities, showing good agreement with a range of experiments.