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## 3D Open Channel Flow Overview

The 3D shallow water equations in AdH can be used to model open channel flow environments such as rivers, estuaries, reservoirs, and coastal regions. Regions of the domain can be 2D, and use the 2D shallow water equations, or 3D. These equations have an assumed hydrostatic pressure distribution. This means that vertical inertia is neglected. This assumption allows AdH (and other shallow water models) to efficiently calculate water depth and velocity for typical open channel conditions. The hydrostatic assumption would be violated near abrupt geometric changes where one might find variations in vertical inertia to be significant. Most open channel models make this assumption, for example, RMA10, CH3D, EFDC.

The model equations can represent the effects of density driven flows such as one would regularly find in estuaries or reservoirs. AdH also includes sedimentation and bed change (morphology). Since AdH utilizes the SEDLIB sediment library it represents noncohesive as well as cohesive sediment processes. (Noncohesive are sands and gravels like one would find in rivers, and cohesives are clays more like the type of problem found in estuaries.) AdH is locally mass conservative and so can be regarded as either a finite volume model or a conservative form finite element model.

Like all modules of AdH, it is portable (multiprocessor, single processor, PC, Unix, Linux, Mac). The equations are represented by a tetrahedral element mesh. From a plan view (from above) the mesh appears as triangles and the mesh in this view is unstructured. In the vertical nodes must be aligned. So in elevation view the mesh is more ordered. It can have different numbers of elements in each column, however, the mesh must be arranged in columns. The most noteworthy aspect of AdH is that the mesh can automatically refine or coarsen. For this module the refinement will always create columns from surface to bed.

Since the mesh is unstructured in the horizontal plane, some very complicated geometry may be represented. The arrangement in the vertical is represented accurately as well. The bed is represented as linear between nodes, and the number of nodes can change. This allows for complex behaviors in density flow, such as a dense plume falling down a slope or salinity intrusion in a navigation channel, can be accurately simulated.

The 3D Shallow Water Module of AdH is currently in the final development stages and is undergoing testing and verification. The module is expected to be released in the near future.