FEQ DOCUMENTATION FIGURES

Diagrams:

1. Branch of a stream system discretized into computational elements
2. An example stream system for illustration of schematic-diagram preparation for the Full EQuations model
3. Schematic of example stream system for input to the Full EQuations model
4. Example dummy branch: (A) dam with spillways and (B) schematic diagram of dam with spillways application in the Full EQuations model
5. Example level-pool reservoir: (A) sketch of level-pool reservoir and (B) schematic diagram of a stream system with level-pool reservoir application in the Full EQuations model
6. Example of a strongly meandering stream for illustration of the approximations of curvilinearity used by the Full EQuations model
7. Example definition of flow lines and cross sections as used in the Full EQuations model
8. Definition of cross-section elevation characteristics
9. Control volume in a stream for unsteady-flow equations
10. Schematic diagram of regions of influence and domain of uniqueness for shallow-water waves in an open channel
11. Required boundary conditions for unsteady flow in open channels for (A) subcritical flow and (B) supercritical flow at the boundaries
12. Explicit finite-difference method on the space-time plane
13. Implicit finite-difference method on the space-time plane
14. Points on the space-time plane for the weighted four-point solution method in the Full EQuations model
15. Control volume (A) plan view and (B) three-dimentional view for abrupt expansion with a diversion channel in a hypothetical stream
16. Example of a typical gate-control function at a control point, as simulated in the Full EQuations model
17. Example of a typical pump-control function at a control point, as simulated in the Full EQuations model
18. Examples of Newton's method of iterative solution for the value of root, X, that results in a function, F(X),value equal to zero (A) under favorable conditions for convergence to the desired root,(B) near point of inflection, (C) with no root, and (D) with root near zero slope
19. Working zones for lower (L) and upper (U) factoring of the coefficient matrix in Full EQuations model simulation
20. Typical vector inner product for row of the lower diagonal matrix in Full EQuations model simulation
21. Typical vector inner product for column of the upper diagonal matrix in Full EQuations model simulation

Graphs:

22. Effect of varying time step,t, on maximum water depth simulated in the Full EQuations model for sewer-pipe experiment 115 (Wallingford Hydraulics Research Station, England) with a fixed distance step,x, of 25 feet
23. Effect of varying time step,t, on maximum water depth simulated in the Full EQuations model for sewer-pipe experiment 115 (Wallingford Hydraulics Research Station, England) with a fixed distance step,x, of 25 feet
24. Effect of varying distance step,x, on maximum water depth simulated in the Full EQuations model for sewer-pipe experiment 115 (Wallingford Hydraulics Research Station, England) with a fixed time step,t, of 3 seconds
25. Simulated and observed maximum water depth and time as a function of distance step,x, for sewer-pipe experiment 115 (Wallingford Hydraulics Research Station, England) with a fixed time step,t, of 3 seconds
26. Simulated and observed water depths for locations 28.4 and 255.7 feet downstream from pipe inlet for scaled sewer-pipe experiment (Wallingford Hydraulics Research Station, England)
27. Simulated and observed water depths for locations 483.0, 710.2, and 937.5 feet downstream from pipe inlet for scaled sewer-pipe experiment (Wallingford Hydraulics Research Station, England)

Fox River:

28. Map showing Fox River, Illinois, study reach and data-collection sites considered in this report
29. Diagram showing bottom elevation and data-collection sites on the Fox River, Illinois, study reach

Fox River Graphs:

30. Measured or rated and simulated discharge and stage at data-collection sites on the Fox River in Illinois
31. Measured or rated and simulated stage-discharge relations at data-collection sites on the Fox River in Illinois for the October 30-November 11, 1990, study period
32. Measured and simulated dye concentrations and discharge at data-collection sites on the Fox River in Illinois

Jacobian Matrix:

33. Single-branch example of the development of the Jacobian matrix of flow and water-surface height for a stream in the Full EQuations model
34. Two-branch example of the development of the Jacobian matrix of flow and water-surface height in a stream in the Full EQuations model
35. Three-branch example of the development of the Jacobian matrix of flow and water-surface height in a stream system in the Full EQuations model
36. Four-branch (with loop) example of the development of the Jacobian matrix of flow and water-surface height in a stream system in the Full EQuations model

Diagrams:

37. Defining control structure for table type 13 in the Full EQuations model
38. Flow variation for a control structure described by table type 13 in the Full EQuations model
39. Flow as a function of tail water for a variable two-node control structure as depicted by table type 13 in the Full EQuations model
40. Defining control structure for table type 14 in the Full EQuations model
41. Flow variation for a control structure described by table type 14 in the Full EQuations model
42. Flow as a function of headwater for a variable two-node control structure, as depicted by table type 14 in the Full EQuations model
43. Major computational steps in the simulation of unsteady flow in the Full EQuations model
44. Location of cross sections for sluice-gate analysis, as simulated in the Full EQuations model