1D–2D Coupled Numerical Model for Shallow-Water Flows

Abstract

This paper presents a new method, the water stage prediction-correction (WSPC) method, based on the theory of characteristics to couple numerical models in the boundary-connected way for shallow-water flows. From the WSPC method, a one-dimensional (1D)–two-dimensional (2D) coupled numerical model is established, which incorporates the artificial porosity method and is thus capable of treating wetting and drying. Details of the 1D submodel and the 2D submodel are given, with special emphasis put on the coupling between the submodels. With the help of the WSPC method, the physically coupled submodels are executed separately and then coupled by means of prediction-correction of the water stages at the coupling units (i.e., where the submodels are linked) so that it is possible to make use of existing submodels with minimum modifications. The convergence of the WSPC method is proved, and the parameter identification is discussed, taking a flat-bottom channel with rectangular cross section as an example. The one-dimensional 1D–2D coupled model is applied to both a hypothetic case and a real-life case in central China, and the results show its validity, stability, and practical reliability.