A comparative study of the cumulant lattice Boltzmann method in a single-phase free-surface model of violent flows

Many coastal and ocean engineering flows, such as tsunamis inundating urban areas, tend to be violent. The characteristics of these damaging flow fields are three-dimensional, highly non-linear and non-hydrostatic. A fully three-dimensional free-surface fluid model is required to simulate such a flow field. Fluid simulations in the field of coastal engineering are often large-scale since large areas are the subject of the simulations. The numerical model must be not only accurate but also efficient. In recent years, the lattice Boltzmann method (LBM) has attracted much attention as a novel simulation method and has been successfully applied to various engineering fields. The LBM calculates complex phenomena in a simple framework. The density field determines the pressure field with the equation of state. This means that the LBM does not have to solve the pressure Poisson equation. However, the existing gas–liquid multi-phase flow models that employ the LBM have a critical problem. Pressure calculations with large density ratios easily become unstable, and the application of these models to violent flow fields is limited. The single-phase free-surface fluid model provides good approximations for flow problems in which the gas dynamics can be neglected. Moreover, the cumulant LBM has attracted attention because it has excellent numerical stability even for high Reynolds number flows. The single-phase free-surface flow model using the cumulant LBM is a suitable approach for simulating violent flow fields in coastal engineering. In this study, we propose a single-phase free-surface flow model based on the cumulant LBM using the volume-of-fluid (VOF) model to capture the interface. We demonstrate that the cumulant LBM is stable under violent flows and reproduces the density field well compared with the traditional single relaxation time model. We find that a larger bulk viscosity can reduce the numerical oscillation of the impact pressure acting on a structure, although a bulk viscosity that is too large reduces the accuracy and stability. The results of the proposed model are in good agreement with previous experimental results.