Efficient GPGPU implementation of a lattice Boltzmann model for multiphase flows with high density ratios

We present the development of a Lattice Boltzmann Method (LBM) for the numerical simulation of multiphase flows with high density ratios, such as found in ocean surface wave and air–sea interaction problems, and its efficient implementation on a massively parallel General Purpose Graphical Processing Unit (GPGPU). The LBM extends Inamuro’s et al.’s (2004) multiphase method by solving the Cahn–Hilliard equation on the basis of a rigorously derived diffusive interface model. Similar to Inamuro et al., instabilities resulting from high density ratios are eliminated by solving an additional Poisson equation for the fluid pressure. We first show that LBM results obtained on a GPGPU agree well with standard analytic benchmark problems for: (i) a two-fluid laminar Poiseuille flow between infinite plates, where numerical errors exhibit the expected convergence as a function of the spatial discretization; and (ii) a stationary droplet case, which validates the accuracy of the surface tension force treatment as well as its convergence with increasing grid resolution. Then, simulations of a rising bubble simultaneously validate the modeling of viscosity (including drag forces) and surface tension effects at the fluid interface, for an unsteady flow case. Finally, the numerical validation of more complex flows, such as Rayleigh–Taylor instability and wave breaking, is investigated. In all cases, numerical results agree well with reference data, indicating that the newly developed model can be used as an accurate tool for investigating the complex physics of multiphase flows with high density ratios. Importantly, the GPGPU implementation proves highly efficient for this type of models, yielding large speed-ups of computational time. Although only two-dimensional cases are presented here, for which computational effort is low, the LBM model can (and will) be implemented in three-dimensions in future work, which makes it very important using an efficient solution.