In this paper, we propose a novel approach for coupling 2D/1D shallow water flow models. Efficiently coupling these models is vital for simulating the flow and flooding of open channels. Currently, existing methods couple the models either at the channel lateral boundaries (lateral methods) or at the location, along the channel flow direction, where the two sub-domains intersect (frontal methods). We classify these methods as horizontal methods since the coupling points are on the horizontal plane. The limitations of these methods include their inability to recover the 2D channel flow structure during flooding without losing efficiency, and their inability to switch between lateral and frontal methods, based on the problem. Here, we propose a new paradigm which is to think of the channel flow as a two layer flow. This leads to the vertical coupling method (VCM) which is able to recover 2D channel flow structure without losing efficiency, switch types depending on the flow and is a superset of some existing methods. The VCM is based on a user chosen elevation above which the user considers the channel to be full. From this elevation, all other flow quantities are defined including the two layers. The flows in the lower and upper layers are assumed to be 1D and 2D respectively, and the appropriate flow models with exchange terms are derived. The 2D shallow water flow model is retained for the floodplains. Finite volume methods (FVM) are formulated for the flood model; the FVM with the operator splitting approach are also formulated to solve and couple the two layer channel flow models. We show that the resulting method (i) is well-balanced (ii) preserves the "no-numerical" flooding property (iii) preserves conservation properties and (iv) adapts to the flow situation.
On Hyperbolic Stochastic Galerkin Projections of Shallow Water Linearised Moment Equations
Bernoulli Institute, University of Groningen（格罗宁根大学伯努利研究所）；CogniGron (Groningen Cognitive Systems and Materials Centre), University of Groningen（格罗宁根大学认知系统材料中心（CogniGron））；Department of Mathematics, Computer Science and Statistics, Ghent University（根特大学数学、计算机科学与统计系）
Variational integrator for the rotating shallow-water equations on the sphere
Memorial University of Newfoundland（纽芬兰纪念大学）；Imperial College London（伦敦帝国学院）；École Normale Supérieure/CNRS, Laboratoire de Météorologie Dynamique（巴黎高等师范学院/法国国家科学研究中心，动态气象实验室）
Water-at-Rest Equilibrium Stability Analysis of a first-moment Shallow Water Exner Moment Model with Sediment Entrainment and Deposition: Extended Technical Report
KU Leuven（荷语鲁汶大学）；Peking University（北京大学）；Ghent University（根特大学）；University of Groningen（格罗宁根大学）
