Long term morphodynamic simulations are used for predicting the impact of climate change and human interventions in our estuarine and coastal regions. The accuracy of this type of simulations suffers generally from low resolution grids. Eventhough high resolution bathymetry data is increasingly more available thanks to new measurement techniques. However, the computational effort for such high resolution simulations is high. Even with increasing computer power and by using the various available techniques for speeding up simulations [Roelvink (2006) ], the computational effort remains high. By introducing a subgrid based method for morphodynamics, we aim at increasing the accuracy of coarse grid based morphodynamic simulations, without significantly increasing the computational effort. Over the last years, we have gained experience in hydrodynamic modelling using subgrid based methods [i.e. Defina (2003), Casulli (2009), Volp et al (2013) ]. These methods combine coarse computational grids with high resolution information. In Volp et al (2013 ) we presented a subgrid based, two-dimensional, depth averaged hydrodynamic model, that is inspired by the method presented by Casulli (2009 ). The model makes use of two grids: a (coarse) computational grid and a high resolution subgrid, see Figure 1. The system of equations is solved at the coarse grid, but high resolution information is taken into account. The water level is assumed to be uniform within a computational cell, but the bed and the roughness are allowed to vary within a cell. Therefore, high resolution effects can be taken into account for the computation of cross-sectional areas, cell volumes, advection and friction. This also implies that cells can be wet, partly wet or dry. The solution based on a coarse computational grid improved significantly, when high resolution effects are taken into account. This result is obtained without a significant increase in computational cost. @en

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.@en

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.@en