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

More documents

Recommendations

Info

126 A Semi-Implicit, Three-Dimensional Model for Estuarine Circulation PHASE ERROR, IN PERCENT MASS PRESERVATION ERROR, IN PERCENT 10 8 6 4 2 0 -1 10 8 6 4 2 0 -1 leapfrog leapfrog-trapezoidal, 1 iteration leapfrog-trapezoidal, 4 iterations 0 10 20 30 40 50 60 Figure 5.20. Continued. Δ t, IN MINUTES
5.2.2.3 Remarks 5. Numerical Experiments 127 The comparison between the error measures for the two-level scheme (niter = 2) and the leapfrog-trapezoidal scheme (one iteration of the trapezoidal step) are given in figure 5.21. The two schemes are very similar in terms of accuracy. The main differ- ence between the two schemes using this test problem was in the performance of the schemes without iteration. Although both schemes suffered from stability problems when iteration was not used, the problems were less troublesome with the leapfrog scheme. The availability of a time filter is an advantage of the three-level scheme. 50 Two of the simulations attempted using the leapfrog scheme could be made stable with this filter without introducing too much damping into the solution. The leapfrog solutions that were stable without smoothing actually improved slightly (had reduced errors) with smoothing because the unsmoothed leapfrog scheme has a slight tendency to amplify the solution to this tidal problem. Several of the unsmoothed leapfrog-trapezoidal solutions with one iteration were unstable; these solutions could be stablized by the filter. Because the computational time required to use the filter is minimal, and the effects on the solution accuracy generally are minimal (and in some cases are beneficial), there is little reason not to employ it routinely in the three-level solutions. Based on the results of both 1-D numerical experiments, it was decided to use the three-level scheme in the 3-D model. 5.3 Three-Dimensional Experiment The 3-D numerical experiment uses a problem presented in a report by Leendertse and Liu (1977) to test the early Rand Cor- poration 3-D model. It simulates a uninodal standing oscillation or seiche (Wilson, 1972) in a rectangular basin. The simple geom- etry and boundary conditions of the problem make it a good test case for the basic computational scheme of a 3-D model. 5.3.1 Seiching in a Rectangular Basin The test basin for the seiching experiment is 46 km long, 14 km wide, and 12 m deep (fig. 5.22). Initially the fluid in the basin is at rest but displaced so that the free surface profile is a half-cosine wave. At the moment the free surface is released, the fluid begins an oscillatory motion that continues until the motion is damped out by frictional resistance. The initial amplitude of the seiche is 25 cm displaced vertically upward at the west (left) end of the basin. The horizontal computational grid for the numerical solution is shown in figure 5.22B; the grid size is Δx = Δy = 2 km. The vertical grid consists of six layers; each layer is 2 m thick. 50 The time filter also is easily added to a 3-D, three-level scheme.
Page 1:
In cooperation with the Interagency
Page 4 and 5:
U.S. Department of the Interior Dir
Page 6 and 7:
This page intentionally left blank.
Page 8 and 9:
vi 4.2 Semi-Implicit One-Dimensiona
Page 10 and 11:
viii Figure 5.6. Graph showing solu
Page 12 and 13:
x Tables Table 2.1. Dimensionless n
Page 14 and 15:
This page intentionally left blank.
Page 16 and 17:
2 A Semi-Implicit, Three-Dimensiona
Page 18 and 19:
Page 20 and 21:
Page 22 and 23:
Page 24 and 25:
10 A Semi-Implicit, Three-Dimension
Page 26 and 27:
Page 28 and 29:
Page 30 and 31:
Page 32 and 33:
Page 34 and 35:
Page 36 and 37:
Page 38 and 39:
Page 40 and 41:
Page 42 and 43:
Page 44 and 45:
Page 46 and 47:
Page 48 and 49:
2.4.1.2 Dynamic Surface Condition 2
Page 50 and 51:
Page 52 and 53:
Page 54 and 55:
Page 56 and 57:
Page 58 and 59:
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Water surface Water surface Level p
Page 70 and 71:
h 1 h 2 h 3 h 4 h 5 h 6 z 1 ⁄ 2 z
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
Page 78 and 79:
Page 80 and 81:
Page 82 and 83:
Page 84 and 85:
Page 86 and 87:
Page 88 and 89:
Page 90 and 91: 76 A Semi-Implicit, Three-Dimension
Page 114 and 115: 100 A Semi-Implicit, Three-Dimensio
Page 190:
176 A Semi-Implicit, Three-Dimensio
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?