GPU-accelerated LBM-VOF two-phase flow simulations with grid refinement

Abstract

The contribution is devoted to a novel grid refinement technique for GPU-accelerated Lattice Boltzmann Method (LBM) dedicated to free surface flow simulations in marine applications. LBM implementations are mostly based on homogeneous isotropic Cartesian discretizations of the computational domain. Challenges occur when a refined spatial and temporal resolution is locally required. To efficiently address this demand, local grid refinement is often deployed to regions featuring small scale structures and effects to be resolved. Within the LBM the spatial and temporal discretizations are strongly coupled. Hence, LBM solvers featuring local grid refinement are suitable for the simulation of transient, turbulent and free surface flows. The present LBM involves a Volume of Fluid (VOF) strategy to model two-phase flows. Herein, the advection of a mixture volume fraction serves to advance the free-surface in time. The employed grid refinement is based on overlapping grids with different resolution. The bidirectional information exchange between the grids is managed via bi[tri]-linear interpolations for two[three]-dimensional simulations. For single-phase flows this synchronisation step comprises the exchange of LBM specific variables solely. When attention is directed to two-phase flows, the inter- grid coupling of the mixture fraction poses a special algorithmic problem. The suggested coupling approach is based on a Piecewise Linear Interface Construction (PLIC) method. Accordingly, the information about the surfaces orientation and position is employed to compute the fill level more accurate within the overlapping regimes. Examples included refer to two- and three-dimensional test cases and reveal that the proposed method is able to reproduce accurate results at fairly moderate computational effort.