A Discrete Boltzmann Model for Transcritical Flows Governed by the Saint-Venant Equations

Based on the Hermite expansion approach, a type of discrete Boltzmann model is devised to simulate the open channel flows governed by the Saint-Venant equations. In this model, a four-discrete-velocity set is adopted, and a local equilibrium distribution with the fourth-order polynomials is kept to simulate the supercritical flows. To numerically solve the kinetic equation, the finite difference method is employed. The model is numerically validated by using four benchmark problems, i.e., dam-break flows, hydraulic jump, steady flow over a bump, and the flume dam-break flows with rectangular and triangular cross-sections. Then, the thin film method is incorporated into the proposed model to deal with the wet-dry boundaries, and this ability has been validated by two cases, i.e., the dam-break flows in a converging–diverging channel and over a triangular obstacle. It is found that the present discrete Boltzmann model can accurately predict the subcritical, transcritical, and supercritical flows with source terms and wet-dry boundaries.