Coupling methods for 2D/1D shallow water flow models for flood simulations.

Efficient methods for the numerical simulation of the shallow water equations are important for understanding flooding events and related phenomena. One such approach is to couple 2D shallow water floodplain flow model to 1D Saint Venant's open channel flow model. Currently, these methods are mostly designed in horizontal fashion, meaning that the separate models are coupled at the horizontal interface between the 2D and 1D regions. These methods cannot be adapted for different flooding scenarios and are not able to compute a 2D flow structure within the channel without solving the full 2D models at all times. In this thesis, we propose coupling methods that aim to overcome these limitations. First, we propose the horizontal coupling method (HCM) in the lines of existing methods. The HCM follows the derivation of coupling terms proposed in [Marin and Monnier, 2009] but we arrive at a slightly different coupling term. Then, a discrete coupling term in closed form and the computation of two lateral discharges over channel cross sections, are proposed. Next, we propose a completely new approach to model coupling; we call it the vertical coupling method (VCM). The VCM is based on vertically partitioning the channel flow into two layers. Flows in the lower and upper layers are assumed to be 1D and 2D respectively, and the appropriate flow models derived. By preserving conservation and 1D consistency, the numerical algorithm for coupling the two layer models, is formulated. We show that (i) both the HCM and the VCM are well-balanced and preserve the no-numerical flooding property, (ii) that the VCM adapts to the flow situation: solving the upper layer 2D model only if flooding. Numerical experiments show that both methods provide promising results and that the VCM is able to compute the 2D flow structure within the channel, whenever flooding. We also discuss (without numerical details) how the VCM is a family of methods and some areas of possible further research work are suggested