A Discrete Boltzmann Approach for Numerical Simulation of Wetting and Drying in Shallow Flows

Zhang, Ting, Peng, Yonghong ORCID: https://orcid.org/0000-0002-5508-1819, Qian, Yu, Zhou, Jianguo ORCID: https://orcid.org/0000-0002-4262-1898 and Yin, Xianfei (2025) A Discrete Boltzmann Approach for Numerical Simulation of Wetting and Drying in Shallow Flows. Water Resources Research, 61 (11). e2025WR041568. ISSN 0043-1397

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Abstract

Wetting and drying processes in shallow-water flows remain challenging to simulate accurately, especially over complex terrain where conventional methods often struggle to maintain stability and precision. To address this gap, a discrete Boltzmann model is developed in this study, incorporating an effective wetting and drying treatment to precisely capture the dynamics of wet–dry boundaries across intricate terrain. The model's performance is evaluated through six benchmark tests, including three one-dimensional (1D) and three two-dimensional (2D) cases: (a) flow in a straight channel with a triangular bed obstacle; (b) propagation of one-dimensional tidal waves across a varying sloped bed; (c) dam-break flow over non-uniform terrain with two elevation steps; (d) 2D dam-break in an L-shaped channel; (e) 2D dam-break flow through a contracting channel; and (f) 2D flooding over terrain with three mounds. The numerical results align well with analytical solutions, previously published computational results, and experimental data. Furthermore, the study highlights the critical role of the wetting threshold water depth in determining both accuracy and numerical stability. An excessively high threshold could result in imprecise predictions of wet–dry transitions, while a threshold set too low may cause numerical instability. Therefore, the appropriate selection of this parameter is essential for obtaining reliable and consistent simulations.