提出一种重叠耦合法(superposition coupling method, SCM)，以高精度地实现基于一维与二维格子Boltzmann方法(lattice Boltzmann method, LBM) 的水动力模型在复杂地形浅水区域的跨维度模拟耦合。对复杂地形区域的浅水水体进行水动力模拟通常涉及跨维度建模，可能会在某些边界处做近似处理，例如河流-湖泊汇合处、洪水淹没区和河口区域。为高效求解跨维度浅水方程 (shallow water equations, SWE)问题，SCM通过在一维和二维LBM模型边界处人工设置重叠区域，使不同维度的2个模型在该区域交换水动力信息。在重叠区域采用零梯度边界条件，从而得到耦合所需的变量。1D-2D耦合模型通过了圆形空腔射流和急弯河道2个验证模型的比较测试，结果显示一、二维耦合模型的精度与二维模型基本相当。本研究通过SCM有效地求解了跨维度浅水方程问题，提高了一维与二维模型间的耦合精度，为复杂地形浅水区域的水动力模拟提供了技术支撑。

A superposition coupling method (SCM) is proposed to achieve high-precision cross-dimensional simulation coupling of one-dimensional and two-dimensional lattice Boltzmann method (LBM) hydrodynamic model. Hydrodynamic simulation of shallow water systems in complex topographic regions often requires cross-dimensional modeling, which can introduce boundary approximation issues, particularly in scenarios such as river-lake junctions, floodplains, and estuary areas. To solve the shallow water equations (SWE) in cross-dimensional scenarios, the SCM involves creating an artificial overlapping zone at the boundary of the 1D and 2D LBM models, facilitating the exchange of hydrodynamic information between the two models. Within this overlapping zone, a zero-gradient boundary condition is applied to derive the necessary variables for coupling. The 1D-2D coupled model was validated against benchmark models for circular cavity jet flow and sharp curved channel flow, demonstrating comparable accuracy to the full 2D model. In shallow water flow numerical simulation, typically different dimensional models are employed based on the topography and topology of the flow, which are crucial factors influencing water body movement. 1D models are generally more efficient for simulating the movement characteristics of large river channels, while 2D models are more suitable for large bodies of water with extensive free surfaces, such as floodplains, lakes, or reservoirs, provided accurate topographic data is available. Consequently, 1D and 2D models are often coupled to leverage their respective advantages. The proposed 1D-2D LBM coupling method utilizes a superposition approach, where the two models share an overlapping zone at their boundary. This zone serves as a buffer for exchanging hydrodynamic information between the models. The zero-gradient boundary condition is applied within the overlapping zone to ensure mass and momentum conservation. The method was implemented by calculating the velocity and depth at the boundaries of the 1D and 2D models and using these values to update the particle distributions within the overlapping zone. This process was iterated until convergence was achieved. The proposed coupling model was evaluated in comparison to benchmark models for circular cavity jet flow and sharp curved channel flow. The results showed that the coupling model produced water depth and velocity profiles that were in good agreement with those of the full 2D model, with minimal differences. The root mean square errors (RMSE) for water depth and velocity were within acceptable ranges, indicating the accuracy and reliability of the coupling method. The superposition approach for coupling 1D and 2D LBM hydrodynamic models provides a robust and efficient solution for simulating shallow water flows in complex topographic regions. The method leverages the strengths of both 1D and 2D models, providing accurate and reliable results while maintaining computational efficiency. The successful application of this method expands the capabilities of LBM in hydrodynamic simulation and demonstrates its potential for solving other multi-dimensional coupling problems, such as 1D-3D coupling or solute transport coupling.