A second-order treatment to the wet-dry interface of shallow water

- We develop a second-order lattice Boltzmann method (1D & 2D) for treating the wet-dry interface of shallow water flows.
- This approach is improved based on the Chapman-Enskog analysis and the Taylor expansion.
- This approach can physically consider the external force terms in the treatment of wet-dry boundary.
- This approach can be used to explore the influence of external forces on long wave run-up.

SummaryThe paper presents a second-order lattice Boltzmann method (LBM) for treating the wet-dry interface of shallow water flows. This approach is improved according to the Chapman-Enskog analysis and the Taylor expansion, which are used to set up the relation of the dry cell and its adjacent wet cell. The external forces, such as bed friction and wind stress, are directly included in the wetting and drying boundary treatment. However, the viscous effect cannot be absolutely removed, as the single relaxation time, τ>0.5, should be retained for the reason of stability. In order to verify the scheme, two one-dimensional (1D) and one two-dimensional (2D) numerical cases are carried out. The results indicate that the approach is superior to the first-order scheme, comparing with the other numerical solutions and the experimental data. It can be concluded that the proposed scheme is more accurate and effective in simulating shallow water fronts.