Sharp numerical simulation of incompressible two-phase flows

Abstract We present a numerical method for simulating incompressible immiscible fluids, in two and three spatial dimensions. It is constructed as a modified pressure correction projection method on adaptive non-graded Oc/Quadtree Cartesian grids, using the level-set framework to capture the moving interface between the two fluids. The sharp treatment of the interface position, of the fluid parameter discontinuities, and of the interfacial jump conditions ensures convergence in the L ∞ -norm. Using a novel construction for the pressure guess, we are able to alleviate the standard time step restriction incurred by capillary forces. The solver is validated numerically and employed to simulate the dynamics of physically relevant problems such as rising bubbles and viscous droplets in electric fields.

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