Three dimensional modeling of free surface flow and sediment transport with bed deformation using automatic mesh motion

This study presents the development of a 3D numerical code for flow-sediment interactions with associated bed changes in free surface flows. To capture the water-air interface, a novel volume of fluid (VOF) formulation is implemented using the ghost fluid method with one-side extrapolation for dynamic pressure. Equations for fluid flow and free surface motion are decoupled due to separation of time scales. Accordingly, time step size can be increased by a factor of 3-orders of magnitude and still preserve numerical stability and computational efficiency. A novel finite area method (FAM) is utilized to discretize Exner equation on irregular bed surface providing a 3D finite volume-like discretization on curved surfaces. The evolution of the water-sediment interface is captured by a novel vertex-based unstructured mesh dynamic motion solve using Laplace operator with variable diffusivity. The code is implemented in foam-extend and tested against two classical experiments. Good results are obtained with correct trends and lower absolute error compared to previous mobile bed models. This shows that the developed code has a good potential of being applied to mobile-bed hydraulic real problems.