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 inner edge of the model domain. The goodness of fit statistics are listed in the below. The model accurately predicts the wave phase but slightly overestimates the amplitude by approximately 0.01 m.

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

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