The widespread availability of high-resolution Digital Elevation Models (DEM), has led to the development of subgrid numerical modeling techniques, based on Shallow Water Equations (SWE). Detailed DEM data is clustered as much as possible within a coarse grid cell that is preferably much larger than a raster pixel. This has considerable advantages for model efficiency, in particular for flood mapping. But overland flow on hills, key to rainfall-runoff, may have several problems with accuracy and stability. These issues arise especially during downhill flooding and with surface runoff on inclined planes. It is the focus of this paper. As robust solutions we propose: (1) a special volume correction equation with intrinsic wetting and drying but without stability constraints and, (2) a simple thin layer calculation that is accurate for runoff on coarse grids with sloping subgrids. Especially the combination (1) and (2) makes the subgrid method highly efficient on slopes, as is demonstrated by a few examples.

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The established method for determining dike heights and dimensioning river training structures is to assess the resulting backwater by numerical modelling. The common consensus is that bottom friction determines the backwater and that momentum advection only has a local effect. We demonstrate that the numerical/artificial backwater contribution from the momentum advection approximation can be of the same order of magnitude as the bottom friction contribution, depending on the advection scheme. This is realized using a one-dimensional analysis and verified using a set of one- and two-dimensional test problems including a wavy bed case, flow over emerged and submerged groynes and finally an actual river. We compare first- and second-order accurate advection schemes and compute their artificial contribution to the backwater, for a range of practically-feasible grid resolutions. The tests demonstrate that the conservation/constancy properties of the scheme determine the size of this contribution, rather than the order of the scheme.@en

Developing strategies to mitigate or to adapt to the threats of floods is an important topic in the context of climate changes. Many of the world’s cities are endangered due to rising ocean levels and changing precipitation patterns. It is therefore crucial to develop analytical tools that allow us to evaluate the threats of floods and to investigate the influence of mitigation and adaptation measures, such as stronger dikes, adaptive spatial planning, and flood disaster plans. Up until the present, analytical tools have only been accessible to domain experts, as the involved simulation processes are complex and rely on computational and data-intensive models. Outputs of these analytical tools are presented to practitioners (i.e., policy analysts and political decision-makers) on maps or in graphical user interfaces. In practice, this output is only used in limited measure because practitioners often have different information requirements or do not trust the direct outcome. Nonetheless, literature indicates that a closer collaboration between domain experts and practitioners can ensure that the information requirements of practitioners are better aligned with the opportunities and limitations of analytical tools. The objective of our work is to present a step forward in the effort to make analytical tools in flood management accessible for practitioners to support this collaboration between domain experts and practitioners. Our system allows the user to interactively control the simulation process (addition of water sources or influence of rainfall), while a realistic visualization allows the user to mentally map the results onto the real world. We have developed several novel algorithms to present and interact with flood data. We explain the technologies, discuss their necessity alongside test cases, and introduce a user study to analyze the reactions of practitioners to our system. We conclude that, despite the complexity of flood simulation models and the size of the involved data sets, our system is accessible for practitioners of flood management so that they can carry out flood simulations together with domain experts in interactive work sessions. Therefore, this work has the potential to significantly change the decision-making process and may become an important asset in choosing sustainable flood mitigations and adaptation strategies.@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.

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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

We present a new modelling strategy for improving the efficiency of computationally intensive flow problems in environmental free-surface flows. The approach combines a recently developed semi-implicit subgrid method with a hierarchical grid solution strategy. The method allows the incorporation of high-resolution data on subgrid scale to obtain a more accurate and efficient hydrodynamic model. The subgrid method improves the efficiency of the hierarchical grid method by providing better solutions on coarse grids. The method is applicable to both steady and unsteady flows, but we particularly focus on river flows with steady boundary conditions. There, the combined hierarchical grid-subgrid method reduces the computational effort to obtain a steady state with factors up to 43. For unsteady models, the method can be used for efficiently generating accurate initial conditions on high-resolution grids. Additionally, the method provides automatic insight in grid convergence. We demonstrate the efficiency and applicability of the method using a schematic test for the vortex shedding around a circular cylinder and a real-world river case study@en