基于格子Boltzmann重叠法求解一、二维耦合浅水动力学模型  

A superposition lattice Boltzmann approach to a 1D-2D shallow water system

作　　者：杨浩 敬玥彤 刘海飞 毕娟[1] 王洪达 褚珣 YANG Hao;JING Yuetong;LIU Haifei;BI Juan;WANG Hongda;CHU Xun(Bejing Academy of Social Sciences,Beijing 100101,China;School of Environment,Beijing Normal University,Bejing 100875,China;Beijing ZEHO Waterfront Ecological Environment Treatment Co.,Ltd.,Beijing 100084,China;Guohuan Tsinghua Environmental Engineering Design&Research Institute Co.,Ltd.,Beijing 100084,China)

机构地区：[1]北京市社会科学院,北京100101 [2]北京师范大学环境学院,北京100875 [3]北京正和恒基滨水生态环境治理股份有限公司,北京100084 [4]北京国华清华环境工程设计研究院有限公司,北京100084

出　　处：《南水北调与水利科技(中英文)》2025年第1期110-117,129,共9页South-to-North Water Transfers and Water Science & Technology

基　　金：北京市社会科学院课题项目(KY2023A0067);国家自然科学基金项目(52079007,52279057)。

摘　　要：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 crossdimensional modeling, which can introduce boundary approximation issues, particularly in scenarios such as riverlake 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 m

关 键 词：格子BOLTZMANN方法 水动力模型 一、二维耦合 重叠法 浅水方程 

分 类 号：TV131.2[水利工程—水力学及河流动力学]