A Semi-Implicit, Three-Dimensional Model for Estuarine ... - USGS

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124 A Semi-Implicit, Three-Dimensional Model for Estuarine Circulation VOLUMETRIC TRANSPORT, IN SQUARE FEET PER SECOND 100 50 -50 -100 100 -50 0 50 -100 0 A B RMS error = 2.8 percent Base solution x= 180,000 feet, Δt = 15 minutes, Δx = 6,000 feet, no smoothing Base solution x = 180,000 feet, Δt = 15 minutes, Δx = 6,000 feet, smoothing = 0.05 0 1.0 2.0 3.0 4.0 5.0 6.0 TIME, IN DAYS Figure 5.19. Solutions using the three-level semi-implicit, leapfrog scheme (no trapezoidal step) (A) with no smoothing and (B) with smoothing (β = 0.05). Without smoothing the run becomes unstable after 4 days. With only minimal smoothing a very good solution is obtained. Δt is the size of the computational time interval. Δx is the size of the computational space interval. RMS, root mean square.
AMPLITUDE ERROR, IN PERCENT ROOT MEAN SQUARE ERROR, IN PERCENT 20 15 10 5 0 -5 20 15 10 5 0 Leapfrog Leapfrog-trapezoidal, 1 iteration Leapfrog-trapezoidal, 4 iterations -5 0 10 20 30 40 50 60 Δt, IN MINUTES Figure 5.20. Solutions using the three-level semi-implicit scheme for the tidal test problem. All simulations used space step Δx = 6,000 feet. The solutions with the leapfrog scheme and the leapfrog-trapezoidal scheme (1 iteration) used smoothing (β = 0.05) for time step Δt ≥ 10 minutes. 5. Numerical Experiments 125
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In cooperation with the Interagency
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U.S. Department of the Interior Dir
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vi 4.2 Semi-Implicit One-Dimensiona
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viii Figure 5.6. Graph showing solu
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x Tables Table 2.1. Dimensionless n
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2 A Semi-Implicit, Three-Dimensiona
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2.4.1.2 Dynamic Surface Condition 2
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Water surface Water surface Level p
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h 1 h 2 h 3 h 4 h 5 h 6 z 1 ⁄ 2 z
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A Semi-Implicit, Three-Dimensional Model for Estuarine ... - USGS

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