Efficiently solving morphodynamics in complex geometies using a mass conservative immersed boundary method on a structured grid.

Abstract:

In this work we propose an efficient approach to solve morphodynamics in complex river geometries, with a particular emphasis for river deltas. We use a novel immersed boundary method of solution in Delft3D, an open source hydrodynamic model that employs a Cartesian structured grid. Our approach employs a hybrid cut-cell/ghost-cell method: ghost cells are used for the flow momentum equations in order to prescribe the correct boundary condition at the immersed boundary, while cut-cells are used in the continuity equation in order to conserve mass. The resulting scheme is robust, does not suffer any time step limitation for small cut cells and conserves fluid mass up to machine precision. The model has been coupled with the existing Delft3D morphodynamic module, adapted for the presence of immersed irregular boundaries cutting through the regular grid. A cut-cell technique is proposed for both the bed-load and suspended load components. The bed-load component, without any modification, turns out to trigger bed instability in small cut-cells, especially for high values of the morphodynamic factor. We therefore propose a simple "virtual merging technique" that guarantees stability even for very high values of the morphodynamic factor. A bank erosion module provides for lateral displacement of the immersed boundaries in proportion to excess bank shear stress. The model has been tested against different analytical and reference solutions. Moreover, morphodynamic simulations of river deltas show that deltas with various channel networks arise as a consequence of jet momentum and stability, and sediment size and geotechnical properties.