One of the main problems in simulating the motion of sharp interfaces between immiscible fluids is a correct description of the transition that occurs when the interfaces merge and reconnect. It is well known that classical methods involving sharp interfaces fail to describe these singular events. We discuss a dissipation free regularization of the classical Euler equations which provides a continuum representation of the interfacial region. An important feature of this model is the nonhydrostatic nature of the stress tensor which gives rise to the effects of surface tension. Our analysis of the simplest topological transitions yields a singularity free description. Joint work with J. Lowengrub.
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