# Wiener Mitteilungen - Band 193

## Three-Dimensional Numerical Modelling of Turbulent River Flow using Polyhedral Finite Volumes

Michael Tritthart

**Thematic Introduction**

In recent years a noticeable trend towards the use of numerical modelling can be observed in all engineering disciplines. This development is not surprising as computer models often feature lower cost than comparable physical experiments, are superior in speed and provide complete information of all relevant quantities throughout the domain of interest at once. The wide field of water-related sciences is no exception to this trend: hydrology has a long-standing tradition in rainfall-runoff modelling, groundwater hydraulics uses solute transport computer models for a long time already, and river hydraulics relies heavily on the use of computational fluid dynamics. The present work will focus on the latter of these important topics.

Especially for the investigation of flow conditions and sediment transport in rivers, computational fluid dynamics proves to be a valuable tool. Compared with physical experiments, it allows for a rapid variation in boundary conditions, including surface roughness and discharge, but also the effect of man-made structures can be quantified very quickly using tools for numerical flow analysis. Hence, they are used in the planning stage of proposed structures or modifications in the river or its surrounding areas, in real-time flood forecasting applications, and they also assist experts in forming their opinion on the reasons of incidents that took place in the past. Depending on the spatial modelling detail, the applications are classified into one-, two-, and three-dimensional models. While the use of 1D-models is widespread among engineers, mostly due to their easy application and the little in-depth knowledge required to apply them, 2D-models are not yet used that frequently. Often they are applied by the engineer to simulate spatially confined flow processes that exceed the application limits of one-dimensional models, for instance the flooding of previously dry terrain where two-dimensional effects prevail. Finally, 3D-models are rarely applied in practice; their use seems to be mostly limited to academia. This is not surprising as the use of higher dimensional models usually requires in-depth knowledge about both the underlying physical processes and the corresponding numerics. Furthermore, a much higher level of detail of the modelled region must be available for a successful application, but very often this data is not at the engineer’s disposal, rendering the gain of 3D-models practically useless.

However, if the required data is available, three-dimensional river analysis codes can become extremely valuable tools for investigating phenomena exhibiting 3D flow characteristics. This includes flow through river bends where a secondary motion is induced (*Nguyen *(2000) [51], *Feurich *(2002) [21]), river junctions (*Bradbrook et al. *(2000) [12]), the presence of submerged groynes (*Ouillon & Dartus *(1997) [60], *Miller et al. *(2003) [48]), scour around obstacles in the flow domain (*Premstaller *(2002) [64]), and also the whole region in the vicinity of weirs and other man-made structures. In all these cases statements about specific flow features, like flow direction and magnitude, the position of the water surface, pressure and turbulent kinetic energy can be made, all of which are crucial for an engineer’s assessment of the situation. The future value of computational fluid dynamics tools clearly is found in predicting sediment transport on a larger scale – especially since the treatment of sediments will be one of the major challenges of the hydraulic engineer in the 21st century – but also water quality investigations and habitat modelling are applications for the time to come, as soon as the required software will have reached a reasonable level of applicability. It should, however, be noted that the correct prediction of the flow field is of paramount importance for the evaluation of any properties that are transported along with the flow. Therefore research efforts that are directed towards improvement of tools for modelling the flow field are still required and will be the primary subject of this work.

Regardless of the dimension of the model or the discretisation technique employed, the flow domain is always decomposed using a computation grid consisting of a large number of smaller entities denoted cells. The common approach is to use triangular or quadrilateral cells in two spatial dimensions, resulting in wedges, pyramids and hexahedra in 3D. Due to the meshing mechanisms employed for this task, the grid forces the location of the respective cell centroids and the user has little control about the actual points where the flow properties are about to be stored. Besides that, the model operator must take reasonable care to align the computation grid with the streamlines in the flow domain to avoid seeing the result affected by a process called numerical diffusion, which will be subject to a detailed discussion later in this work. However, such an alignment is not always straightforward or even possible if a dominating flow direction cannot be identified.

This thesis proposes a paradigm shift in grid generation that comes at hand for circumventing some of the mentioned problems associated with widely used meshing techniques. It derives and prepares the required algorithms for creating computation grids based on point distributions given by the model user, enabling the operator to be in full control over the storage locations of the flow properties he is interested in. The grid generator subsequently fulfils the task of creating a mesh using the given point set, applying rules of neighbourship as fundamental base for its workflow. This results in cells featuring an arbitrary number of edges in 2D and associated faces in 3D. These cells are based on logic generation rules and allow for the exchange of mass between a larger number of cells if an appropriate point distribution was chosen, thus reducing the negative effects of flows not perpendicular to cell faces. This can be advantageous in situations where no prevailing flow direction can be identified, as in recirculating flows or in the case of flows in floodplains when multiple streams interact with each other (*Tritthart & Milbradt *(2003) [81]), but also in any other flow situation exhibiting a strong secondary motion, as will be shown later.

Michael Tritthart

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