Full Equations (FEQ) Model for the Solution of the Full, Dynamic Equations of Motion for One-Dimensional Unsteady Flow in Open Channels and Through Control Structures
Purpose: Optional block given only if GEQOPT = STDW or STDCW appears in the Run Control Block (section 13.1) or if these options appear for one or more branches. Only those branches that require the information must be included in the input. The controlling values of depth and the rule for interpolation for the variable weight in the distance integral approximation are given with this block to increase the robustness of computations at shallow depths.
Heading:One line of user-selected information. The suggested string is NEAR-ZERO DEPTH.
LINE 1Variable: HEAD
Format: A80
Example: BRAN YATONE YATHAF INTERP
Explanation:These are user-supplied headings for subsequent information on Line 2.
LINE 2
Variables: BRAN, YATONE, YATHAF, CHAR8
Format: I5, 2F10.0, A8
Explanation:The parameters to improve computational robustness when simulating near-zero depths are specified on this line. A set of parameters must be input for each branch for which GEQOPT=STDW or STDCW is used so that Line 2 is repeated for each of these branches.
BRAN is the branch number,YATONE is the water-surface height below which selected distance-integral approximations are fully off-centered,
YATHAF is the water-surface height above which these approximations are again fully centered,
CHAR8 is an option for interpolation between the two limiting values for centering. The interpolation options are LINEAR or linear for linear interpolation, CUBIC or cubic for cubic interpolation, and left blank for linear interpolation. For cubic interpolation, the rate of change of the off-centering weight with respect to water-surface height at the limiting values is always zero.
A computational element is off-centered whenever the minimum water-surface height falls below YATHAF for that branch. The off-centering of the integral approximations reduces the accuracy of the approximations but increases the computational robustness. This approach is applied on the basis of the result that depths near zero are not of primary interest but are often the primary source of computational problems. Reducing the accuracy of the computations at these shallow depths will have little effect on the results at the depths of interest.
The off centering of the integral approximations has been tested only on a few streams simulated in FEQ, but simulation of flow values approaching zero has been successful. The values to choose for YATONE and YATHAF are not yet clear. A preliminary guideline is that YATHAF should be close to the depth that results when flows become of interest. Clearly it should be less than bankfull stage for the branch. The YATONE value should be much less than bankfull stage but yet not so small that the stream is dry before the depth given by YATONE is reached.