2DH two-layer shallow-water model for flows over mobile beds with erodible banks

Abstract

The collapse of a dam induces a fast transient flow that may interact with the erodible bed and banks of the downstream river, entraining large amounts of sediments and modifying the valley morphology. It may constitute a danger for the surrounding inhabitants and infrastructures. To reduce the catastrophic consequences of such an event, the decision-makers need tools to assess the risk posed by a dam and to prepare emergency plans. This thesis presents a numerical model aimed at simulating such transient flows over mobile beds. The two-dimensional horizontal (2DH) two-layer shallow-water model considers an upper clear-water layer and a lower bed-load transport layer flowing on a motionless sediment bed. The depth-averaged velocities in both layers are assumed distinct in norm and direction. Distinct granular concentrations are assumed in the bed-load layer and in the motionless bed. The mass and horizontal momentum balances are written in each layer. Through the source terms, vertical mass and momentum transfers may occur between the layers following erosion / deposition. The conservative part of the governing equations is shown to be hyperbolic. The set of equations is solved on unstructured triangular meshes by a finite-volume scheme with a LHLL solver. Several boundary conditions can be handled. A bank-failure operator is inserted in the model. It compares local bank slopes with threshold values and tilts the unstable elements until they reach a repose angle. The model is validated against theoretical and experimental results of dam-break flows over sand beds, e.g. in an enlargement, on a floodplain and in a prismatic flume.(FSA 3) -- UCL, 201