A mass-conserving, cut-cell moving-bed model for scour simulation

We propose a moving-bed, cut-cell model to simulate scour with an existing unstructured-grid Navier-Stokes solver. The computational mesh includes cells in the water and within the bed, and the interface between them is set as the top of the sediment layer and moves due to erosion and deposition. Although the horizontal grid is unstructured, a Cartesian coordinate system is used in the vertical to avoid problems related to steep slopes when using curvilinear, bottom-following grids. To better represent the bathymetry, the cut-cell method is used in which finite-volume cells near the bottom are cut to ensure that the faces are aligned with the bed. To eliminate discontinuous shear caused by small cut cells at the bed, the re-mapping method is used. The Exner sediment mass balance equation is solved at the vertices of the unstructured grid cells while bedload tranpsort is computed tangential to cell faces and erosion and deposition are computed at cell centers. These components of sediment transport are incorporated into the model in a way that ensures conservation of total (suspended + bedload) sediment mass. We demonstrate that the model reproduces scour patterns for lab test cases and conserves sediment mass to machine precision.