There is growing interest in developing mathematical models and appropriate numerical methods for problems involving networks formed by, essentially, one-dimensional (1D) domains joined by junctions. Examples include hyperbolic equations in networks of gas tubes, water channels and vessel networks for blood and lymph in the human circulatory system. A key point in designing numerical methods for such applications is the treatment of junctions, i.e. points at which two or more 1D domains converge and where the flow exhibits multidimensional behaviour. This paper focuses on the design of methods for networks of water channels. Our methods adopt the finite volume approach to make full use of the two-dimensional shallow water equations on the true physical domain, locally at junctions, while solving the usual one-dimensional shallow water equations away from the junctions. In addition to mass conservation, our methods enforce conservation of momentum at junctions; the latter seems to be the missing element in methods currently available. Apart from simplicity and robustness, the salient feature of the proposed methods is their ability to successfully deal with transcritical and supercritical flows at junctions, a property not enjoyed by existing published methodologies. Systematic assessment of the proposed methods for a variety of flow configurations is carried out. The methods are directly applicable to other systems, provided the multidimensional versions of the 1D equations are available.
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）
