A multi-phase flow method with a fast, geometry-based fluid indicator

We present a novel methodology for incompressible multi-phase flow simulations in which the fluid indicator is a local signed distance (level set) function, and front-tracking is used to evaluate accurately geometric interfacial quantities and forces. Employing ideas from Computational Geometry, we propose a procedure in which the level set function is obtained at optimal computational cost without having to solve the level set equation and its associated re-initialization. This new approach is robust and yields an accurate and sharp definition of the distinct bulk phases at all times, irrespective of the geometric complexity of the interfaces. We illustrate the proposed methodology with an example of surface tension-mediated Kelvin-Helmholtz instability.