6.6 Computational Mesh
6.6.2 Description
This section describes computational mesh construction specific to the 3D hydrodynamic simulation class. This mesh construction is a direct extension of that described in Section 5.12 in that the following are required.
- Specification of a 2D mesh (as per Section 5.12), and
- Specification of a vertical discretisation implementation (extension of 2D HD, this section)
The vertical discretisation implementation determines the manner in which a 2D model is extended to 3D. Supported vertical discretisation implementations are summarised in Table 6.5, with links to the relevant implementation sections below. The required commands for these implementations are summarised in Table 6.6.
| Model Implementation | Description |
|---|---|
| Sigma | The default vertical mesh for 3D simulations. Uses terrain following sigma layers and supports wetting and drying. |
| Z | Uses fixed elevation z layers with a configurabled number of surface sigma layers. Suited to density stratification studies where wetting and drying is confined to the surface sigma layer range only. |
| Command | Description |
|---|---|
| Layer Face File | Conditional - Required for the 3D simulation class. Specifies the CSV file containing the vertical face distribution used by the selected vertical mesh type. |
| Vertical Mesh Type | Conditional - Required for the 3D HD simluation class. Selects the vertical discretisation method for the 3D mesh. Defaults to Sigma if not specified |
| Surface Sigma Layers | Optional - Sets the number of surface sigma layers for the Z vertical mesh type. Defaults to 1 if not specified. |
| Minimum Bottom Layer Thickness | Optional - Sets a minimum allowable bottom layer thickness to improve numerical robustness in shallow bottom cells. Not applicable to the sigma vertical mesh type. |
| Cell 3D Depth | Optional - Sets the depth threshold below which 3D momentum calculations are disabled while mass flux calculations are maintained. Useful for model stability in shallow water depths. |
6.6.3 Sigma
The sigma implementation assigns the same number of vertical layers at every 2D cell. These layers follow the bed profile across the model domain and together occupy the entire water column (see Figure 6.1). As such, they generally vary spatially in their absolute thickness and in the elevations of their upper and lower faces. Sigma layers are useful for simulating boundary layer problems with a low computational overhead and for capturing areas of wetting and drying. Sigma layers are often not well suited to the simulation of vertical density stratification. Fixed z layers should generally be used in these instances (see Section 6.6.4).
Figure 6.1: Sigma Vertical Mesh
A Layer Face File is also required to set the relative rather than absolute vertical distribution of sigma layers across the water column. This file is a CSV file with one column headed SIGMA. Each row contains a decimal number less than 1.0 (water surface) and greater than 0.0 (bed) that sets the elevation of the layer face as a fraction of the water column. Decimal numbers must be monotonically decreasing from the second row. If this command is not issued, no sigma layers will be assigned and the model will run in 2D.
In very shallow (but not dry) regions, 3D momentum calculations can be turned off to support stability and speed of computation. The water depth at which this occurs can be set manually. Mass flux calculations are preserved.
Example sigma layer face file with five evenly distributed layers.
LF_Sigma_001.csv
SIGMA
0.8
0.6
0.4
0.2Example sigma layer face file with seven unevenly distributed layers, with higher resolution towards the bed.
LF_Sigma_002.csv
SIGMA
0.9
0.8
0.6
0.2
0.1
0.056.6.4 Z
The Z implementation assigns vertical layers at fixed absolute heights across the entire model. These layers are horizontal and are useful for simulating vertical density stratification (see Figure 6.2). Z layers cannot wet and dry so specified heights must be always less than the minimum expected surface water level. To allow for surface water level changes and wetting and drying, one sigma layer is activated by default, and this layer occupies the vertical range between the uppermost (fixed and user specified) Z layer and the dynamically computed water surface.
Figure 6.2: Z Vertical Mesh With Surface Sigma Layers
A Layer Face File is also required to set the absolute vertical heights of Z layers across the water column. This file is a csv file that has one column, with header Z. Each row has a decimal number that sets the absolute elevation of the layer face in the datum of the bathymetry. Decimal numbers must be monotonically decreasing from the second row. If this command is not issued then no layers will be assigned and the model will run in 2D.
If additional vertical resolution is required above the fixed Z layers then multiple sigma layers can be specified. These layers automatically fill the vertical distance between the uppermost Z layer face and surface water level, with an equal vertical distribution. This surface sigma layer distribution is not user specifiable.
In some instances, the fixed Z layer heights may generate very shallow bottom layer cells when applied to bathymetric data. For example, a Z layer face specified at -10.6m against a bathymetric bed elevation of -10.61m will generate a bottom cell depth of 0.01m. This may cause computational difficulties, so can be overridden such that the cell depth is increased locally (by lowering bathymetry) to a user specified minimum.
Example Z layer face file. Z elevations are aboslute elevation (mRL).
LF_Z_001.csv
Z
-0.5
-1.0
-2.0
-5.0
-10.0