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In this paper we propose an efficient second order well balanced finitevolume method for modeling complex free surface flows at the aid of a simplediffuse interface method. The employed physical model is a two-phase modelderived from the Baer-Nunziato system for compressible multi-phase flows. Inparticular, as proposed for the first time in Dumbser (2011), the number ofequations is reduced from seven to three by assuming that the relative pressureof the gas with respect to the atmospheric reference pressure is zero, and thatthe gas momentum is negligible compared to the one of the liquid. The two-phasemodel does not make any of the classical assumptions of shallow water typesystems, hence it does not neglect vertical accelerations and the free surfaceis not constraint to be a single-valued function, so even complex shapes asthose of breaking waves can be properly captured. The resulting PDE system issolved by a novel well balanced path-conservative finite volume method onstructured Cartesian grids, which is able to preserve exactly the equilibriumstates even in the presence of obstacles. It furthermore automatically computesthe location of the water-air interfaces, and assures low numerical dissipationat the free surface thanks to a novel Osher-Romberg-type Riemann solver.Finally, high computational performance is guaranteed by an efficient parallelimplementation on a GPU-based platform that reaches the efficiency of twentymillion of volumes processed per seconds and makes it possible to employ evenvery fine meshes. The validation of our new well balanced scheme is carried outby comparing the obtained numerical results against existing analytical,numerical and experimental reference solutions for a large number of testcases, among which oscillating elliptical drops, dambreak problems, breakingwaves, over topping weir flows, and wave impact problems.

A well balanced diffuse interface method for complex nonhydrostatic free surface flows