An improved two-phase Lattice Boltzmann model for high density ratios: application to wave breaking

A new Lattice Boltzmann method (LBM) is developed to efficiently simulate multiphase flows with high density ratios, in order to study complex air-sea interaction problems, such as wind wave breaking and related sea-spray generation. In this method, which builds and improves on the method proposed earlier by Inamuro et al. (2004b), the motion of (diffusive) interfaces between fluids is modeled by solving the convective Cahn-Hilliard equation with the LBM. As in the latter work, we eliminate instabilities resulting from high density ratios by solving an additional Poisson equation for the fluid pressure. The resulting numerical scheme is computationally demanding since this equation must be solved over the entire computational domain, which motivates implementing the method on the massively parallel environment offered by General Purpose Graphical Processing Units (GPGPU), via the nVIDIA CUDA framework. In this paper, we present the equations and numerical methods for the method and the initial validation of the resulting multiphase-LBM for standard benchmark problems such as Poiseuille flow, a rising bubble, and Rayleigh-Taylor instability for two-fluid systems. A good agreement with the reference solutions is achieved in all cases. Finally, the method is applied to simulating an ocean breaking wave in a space periodic domain. In all the presented applications, it is observed that the GPGPU implementation leads to speed-ups of about two orders of magnitude in comparison to a single-core CPU implementation. Although the method is only currently implemented in a two-dimensional (2D) framework, its extension to three-dimensions (3D) should be straightforward, but the need for the efficient GPGPU implementation will become even more drastic in 3D.