2018/06/13 by Elena Gaburro, Manuel J. Castro, Gaburro, Elena +3
Engineering · Earth and Planetary Sciences · #Fluid Dynamics Simulations and Interactions #Coastal and Marine Dynamics #Computational Fluid Dynamics and Aerodynamics
paper · pdf · doi:10.48550/arxiv.1806.04960
In this paper we propose an efficient second order well balanced finite\nvolume method for modeling complex free surface flows at the aid of a simple\ndiffuse interface method. The employed physical model is a two-phase model\nderived from the Baer-Nunziato system for compressible multi-phase flows. In\nparticular, as proposed for the first time in Dumbser (2011), the number of\nequations is reduced from seven to three by assuming that the relative pressure\nof the gas with respect to the atmospheric reference pressure is zero, and that\nthe gas momentum is negligible compared to the one of the liquid. The two-phase\nmodel does not make any of the classical assumptions of shallow water type\nsystems, hence it does not neglect vertical accelerations and the free surface\nis not constraint to be a single-valued function, so even complex shapes as\nthose of breaking waves can be properly captured. The resulting PDE system is\nsolved by a novel well balanced path-conservative finite volume method on\nstructured Cartesian grids, which is able to preserve exactly the equilibrium\nstates even in the presence of obstacles. It furthermore automatically computes\nthe location of the water-air interfaces, and assures low numerical dissipation\nat the free surface thanks to a novel Osher-Romberg-type Riemann solver.\nFinally, high computational performance is guaranteed by an efficient parallel\nimplementation on a GPU-based platform that reaches the efficiency of twenty\nmillion of volumes processed per seconds and makes it possible to employ even\nvery fine meshes. The validation of our new well balanced scheme is carried out\nby comparing the obtained numerical results against existing analytical,\nnumerical and experimental reference solutions for a large number of test\ncases, among which oscillating elliptical drops, dambreak problems, breaking\nwaves, over topping weir flows, and wave impact problems.\n