Long wave propagation

Analytical Solution

The purpose of this verification test is to assess the model performance in simulating long wave propagation. The case is also useful for testing the model performance and symmetry for a non-rectangular domain. The test case consists of a quarter annulus shaped domain with a linear bottom in the radial direction. The analytical

Setup

Figure 1. Quarter Annulus

• Forcing: 0.3048 m amplitude M2 tide (red cell string)
• Bottom friction: 0.0 sec/m^(1/3) (Manning N)
• Horizontal eddy viscosity: :0 m^2/sec
• Run duration: 5 days
• Ramp period: 2 days
• Time step: 10 min
• Wall Friction: Off
• Grid resolution: 1000 x 1000 m (constant)
• Number of cells: 23409

Results

The figure below shows a time series of water levels at the green point shown in the figure above.

Table 2. Goodness of fit statistics for the water elevation

Statistic	Value
RMSE	0.014 m
RMAE	0.028
R^2	0.999
Bias	0.003 m

Figure 2. Comparison of analytical and calculated water surface elevations and bed elevations.

References

• Lynch, D.R., and Gray, W.G. (1978). "Analytical solutions for computer flow model testing," J. Hydraulics Division, 104, 1409-28.

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Test_Cases