An interface tracking finite element methodology is presented for 3D turbulent flow fluid-structure interaction, including full-friction contact and topology changes, with specific focus on heart valve simulations. The methodology is based on a unified continuum fluid-structure interaction model, which is a monolithic approach, where the fundamental conservation laws are formulated for the combined fluid-structure continuum. Contact is modeled by local phase changes in the unified continuum, and computational results show the promise of the approach. The core algorithms are all based on the solution of partial differential equations with standard finite element methods, and hence any general purpose finite element library which can leverage state of the art hardware platforms can be used for the implementation of the methodology.