A subgrid based approach for morphodynamic modelling

• Presenting an accurate and efficient method for morphodynamic simulations.
• Different grid resolutions are used for the hydro- and morphodynamic computations.
• An upwind discretisation scheme based on the direction of the bed celerity.

To improve the accuracy and the efficiency of morphodynamic simulations, we present a subgrid based approach for a morphodynamic model. This approach is well suited for areas characterized by sub-critical flow, like in estuaries, coastal areas and in low land rivers. This new method uses a different grid resolution to compute the hydrodynamics and the morphodynamics. The hydrodynamic computations are carried out with a subgrid based, two-dimensional, depth-averaged model. This model uses a coarse computational grid in combination with a subgrid. The subgrid contains high resolution bathymetry and roughness information to compute volumes, friction and advection. The morphodynamic computations are carried out entirely on a high resolution grid, the bed grid. It is key to find a link between the information defined on the different grids in order to guaranty the feedback between the hydrodynamics and the morphodynamics. This link is made by using a new physics-based interpolation method. The method interpolates water levels and velocities from the coarse grid to the high resolution bed grid. The morphodynamic solution improves significantly when using the subgrid based method compared to a full coarse grid approach. The Exner equation is discretised with an upwind method based on the direction of the bed celerity. This ensures a stable solution for the Exner equation. By means of three examples, it is shown that the subgrid based approach offers a significant improvement at a minimal computational cost.

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