Flows with moving interfaces appear in a wide range of real world problems. This report, accompanying the video Two fluids level set: High performance simulation and post processing" presents the implementation of a Level Set method for two fluid flows in the parallel finite element code Alya that can scale up to thousands of processors. To give an idea of the versatility of the implementation examples extending from the flushing of a toilet to the simulation of free surface flows around ship hulls are presented. The spatial discretization is based on unstructured linear finite elements, tetrahedras and prisms that allow a great degree of flexibility for complex geometries as will be shown in the examples. The time discretization uses a standard trapezoidal rule. The position of the moving interface is captured with the Level Set technique that is better suited for complex flows than interface tracking schemes. The jump in the fluid properties is smoothed in a region close to the interface. For ship hydrodynamics simulations the model has been coupled with the SST k-? turbulence model.