We demonstrate the capabilities of an automatic, adaptive, local or global, remeshing algorithm developed for flows with interfaces and/or moving boundaries by using it in the context of two-dimensional unsteady interfacial flows with surface tension. Our formulation solves the Navier-Stokes equations using the finite element method, a front-tracking approach to represent the interface and an Arbitrary Lagragian-Eulerian formulation coupled with a pseudo-solid approach to handle the deformation of the underlying computational grid. Verification and validation cases are run to ensure that the code correctly implements the right equations for the problems at hand and that physically-meaningful results can be obtained with the models and methods used. The capabilities of the algorithm in handling large-scale displacements and deformations of the fluid-fluid interfaces and its ability to efficiently and accurately capture the small-scale, high-frequency phenomena that appear in this class of problems is investigated on two problems which feature Rayleigh-Taylor and Kelvin-Helmholtz instabilities.
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