Discrete Boltzmann Modeling of Two‐Layer Shallow Water Flows

Abstract

Within the framework of discrete Boltzmann modeling (DBM), a two‐layer discrete Boltzmann model (D2Q16‐2) is proposed for the simulation of shallow water flows, aiming to overcome the limitations of conventional depth‐averaged models in representing layered flow structures and the reduced numerical stability of classical lattice Boltzmann methods under supercritical flow conditions. The proposed model extends the single‐layer shallow water DBM by explicitly introducing an interlayer coupling force to describe momentum exchange between layers. In addition, a dynamic wetting–drying treatment based on a characteristic water depth threshold is incorporated to enhance numerical robustness under complex hydraulic conditions. The performance of the model is assessed using eight classical benchmark problems, including one‐dimensional (1D) and two‐dimensional (2D) dam‐break flows, density‐driven gravity currents, and flows over inclined beds and complex topography. The numerical results show that the D2Q16‐2 model is able to stably simulate free‐surface evolution, interlayer interface dynamics, and wetting–drying processes across a range of flow conditions. In general, the proposed model exhibits reasonable accuracy and numerical stability for two‐layer shallow water flows, and provides a feasible mesoscopic framework for representing layered flow structures within a depth‐averaged formulation.