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This paper presents a new monolithic free-surface formulation that exhibitscorrect kinetic and potential energy behavior. We focus in particular on thetemporal energy behavior of two-fluids flow with varying densities. Correctenergy behavior here means that the actual energy evolution of the numericalsolution matches the evolution as predicted by the discrete two-fluidequations. We adopt the level-set method to describe the two-fluid surface. Toensure the correct energy behavior we augment the interface convection equationwith kinetic and potential energy constraints. We solve the resultingformulation consisting of the fluid and interface equations in a monolithicfashion using a recently proposed level-set method [I. Akkerman. Monotonelevel-sets on arbitrary meshes without redistancing. Computers & Fluids,146:74-85, 2017.]. For the spatial discretization divergence-conforming NURBSare adopted. The resulting discrete equations are solved with a quasi-newtonmethod which partially decouples the constraints from the rest of the problem.The simulation of a dambreak problem numerically supports the correct energybehavior of the proposed methodology. This improves the solution qualitysignificantly upon a more traditional approach. Due to the excellent accuracyper degree of freedom one can suffice with a much lower resolution.

Toward free-surface flow simulations with correct energy evolution: an isogeometric level-set approach with monolithic time-integration