A conservative sharp interface method for incompressible viscous two-phase flows with topology changes and large density ratio

Topology change of interfaces often leads to unresolved interface structures such as tiny droplets/bubbles, which requires the regularization of the order parameter and consequently causes artificial modification of volume fraction of the fluids. This could give rise to unphysical oscillation of pressure and cause the failure of computation, in particular for two-phase flows involving large density ratio. We develop a robust conservative sharp-interface method for incompressible viscous two-phase flows with topology changes and large density ratio. The method consists of a cut-cell meshing approach that dynamically generates unstructured meshes in the vicinity of the interface, a second-order finite volume scheme in the Arbitrary Lagrangian- Eulerian framework, and a projection method. The jump conditions at the interfaces are incorporated into the calculation of fluxes at the cell faces of the unstructured meshes that coincide with the reconstructed interfaces, to ensure that they are strictly satisfied at the interface. Unlike a pseudo-compressible formulation used in the previous study, the projection method prevents the oscillation of pressure in the presence of topology change. Special treatments are proposed to further improve the robustness of the method when dealing with unresolved interface structures, including removal of tiny droplets, adjustment of spatial discretization and restriction of the maximum curvature calculated. In such a way, two-phase flows involving topology change and large density ratio can be numerically resolved in a sharp-interface, efficient and robust manner. The performance of the proposed method is systematically examined by a series of numerical tests, including spurious currents, oscillation of a suspended droplet, droplet deformation in shear flows, breakup of a liquid thread, rising bubbles and partial coalescence of a droplet with a pool. The numerical results are compared against analytical solution, benchmark results or experimental data, and good agreement has been achieved.