A regularized single-phase lattice Boltzmann method for free-surface flows

Abstract In this paper, a lattice Boltzmann (LB) scheme for simulating free-surface flows is investigated, in which the Hermite expansion-based regularization (Zhang et al., 2006) and the single-phase free-surface model (Korner et al., 2005) are adopted. It is pointed out that the original free-surface model may encounter some conflicting situations when dealing with some extreme cases, such as adjacent filled/empty interface cells, isolated interface cells, and how to reconstruct distribution functions if too few non-gas cells are available in the neighbourhood region. An alternative reconstruction method based on the extrapolation and the gradient of macroscopic variables is then proposed to tackle these problems. The proposed numerical framework is validated through several test-cases, from which it is shown that the regularization can largely improve the stability of LB simulations of violent free-surface flows such as dam-break flows. In addition, the proposed reconstruction method can help further reduce the spurious pressure noises in regularized LBM. Nevertheless, a more dissipative behaviour has been observed in the viscous standing wave test-case.

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