Anisotropic mesh adaptation is a key feature in many numerical simu- lations to capture the physical behavior of a complex phenomenon at a reasonable computational cost. It is a challenging problem, especially when dealing with time dependent and interface capturing or tracking problems. In this paper, we describe a local mesh adaptation method based on an extension of the Delaunay kernel for creat- ing anisotropic mesh elements with respect to adequate metric tensors. In addition, we show that this approach can be successfully applied to deal with fluid-structure inter- action problems where parts of the domain boundaries undergo large displacements. The accuracy and efficiency of the method is assessed on various numerical examples of complex three-dimensional simulations.