Hybrid Shallow Water/3D Flow Model
This article highlights developments to be released in FLOW-3D version 10.1.
A shallow flow model has been available in FLOW-3D for many years. The model is suitable for flows in which horizontal extents are much larger than the depth. Examples include flow in the sea, estuaries, large lakes, seasonal floods, liquid coatings, lubricating films, and water on automobile windshields.
The three-dimensional Navier-Stokes equations reduce to 2D depth-averaged ones referred to as the shallow water model . This approach successfully captures free surface waves, flooding of a complex terrain, laminar and turbulent flows and even surface tension forces. Its main strength is the ability to efficiently model large-scale shallow flows.
Naturally, the shallow water approximation is not suitable to model flow having significant vertical accelerations, for example, around essentially 3D structures that often exist in a ‘shallow water’ environment, such as bridges, drilling rigs at sea and dams in reservoirs. Therefore, it is desirable to be able to combine both shallow water and 3D type flows in the same simulation.
The hybrid shallow water/3D flow model in FLOW-3D is designed for just that purpose. The approach takes advantage of multi-block meshing, where a mesh block is designated as type shallow water or 3D. The standard shallow water or 3D equations are solved within each such block, based on the user selection, and the respective solutions are coupled at the block boundaries. Standard linked and nested mesh block arrangements are allowed (e.g., see Fig. 1), except that shallow water type nested blocks are not allowed inside a 3D mesh block.
Figure 1. Example of an arrangement of two 3D mesh blocks
(a linked one and a nested one, shown in red) and a shallow water block.
The coupling is done differently between mixed linked blocks and mixed nested-containing blocks. The solution between linked blocks is coupled in a two-way fashion, with data passed in both directions, so that flow can take place in either direction.
For a mixed nested block case (the nested block is type 3D and the containing one is type shallow water), the solution is passed only from the containing block to the nested block; the shallow water solution in the containing block ‘does not know’ about details computed in the 3D nested block.
Example: Flooding of a Large Area
This example describes flooding of a large area, with flow originating at a weir. The weir, which can be recognized as an example simulation provided with the FLOW-3D installation, is modeled with a full 3D model, while the flooded area downstream, containing several simple structures, is described with the shallow water equations (Fig. 2). The two mesh blocks are adjacent to each other, i.e., they are linked.