A curved boundary treatment for discrete Boltzmann model of shallow water flows based on a partially saturated method

Abstract

In the present study, a boundary treatment scheme named the partially saturated method (PSM) is incorporated into the discrete Boltzmann model (DBM) for shallow water flows to deal with complex curved boundaries. In this PSM-DBM, the two-dimensional 16 velocity levels scheme is adopted and the finite difference method is used to solve the governing equation. Then, the PSM-DBM has been applied to simulate four cases, i.e. such as steady flow in a bending channel, the flow past a stationary cylinder, a jet-forced flow in a circular basin and flow in a meandering channel with 90° consecutive bends. The simulated results have been compared with the experiments and the simulation by traditional numerical simulation. The study shows that the agreement between simulation and experiments is good. It is demonstrated that the PSM-DBM is stable and accurate to deal with the curved boundaries. Moreover, the implementation of the PSM is relatively straightforward in treating stationary curved geometries and is easy to be incorporated into the DBM for shallow water flows. In conclusion, the proposed PSM-DBM can be used widely for flows with curved boundaries.