NUMERICAL MODEL DESCRIPTION
Model description and capabilities
A numerical model, called THKFUL, was developed on the basis of the one-
dimensional, fully coupled equations presented in the Formulation section. The
model, written in the FORTRAN programming language, computes the unsteady
water depth, velocity, ice thickness, and ice velocity for a river channel. The current
version of THKFUL assumes a prismatic, rectangular channel with uniform bed
slope, constant values of bed and ice roughness, and invariant and uniform ice
properties.
The model THKFUL calls on many subprograms to do various computational
tasks. A file utility subprogram opens all required input and output files. Another
subprogram reads all the channel geometry, ice property, and physical constant
data. One subprogram reads the initial conditions file of depth, velocity, ice thick-
ness, and ice velocity at each cross section. Another reads the new boundary condi-
tion data at the beginning of each time step. The stability of the ice cover at each
cross section, assessed by means of a force accumulation, is determined using
another subprogram. One of two equation-system solvers is called to compute flow
and jam variables. FULSOL fills the coefficient matrix using the technique described
in the Formulation section for the simultaneous solution of the four dependent vari-
ables. However, if the entire ice cover is found to be stable, only the water variables
are calculated by WATUNC, which fills and solves a smaller coefficient matrix.
Another subprogram writes data to three output files with user-definable write
intervals. The first output file provides a listing of the depth, velocity, ice thickness,
and ice velocity at each cross section at the specified print interval. The second
output file provides profile data for the bed, bottom, and top of the ice cover, and
water level at the specified print interval. The third output file contains data neces-
sary for compiling animated plots of the profiles with time. A full program listing
can be found in Zufelt and Ettema (1996).
Another program, called UNCTHK, is very similar to THKFUL, but operates in
a loosely coupled mode. The ice and water variables are calculated separately and
sequentially. In this model, the ice variable solver, ICEUNC, is called one or more
times (as specified by the user) for each time that the water solver, WATUNC, is
called. This modification was made because the ice variables can change rather
abruptly, e.g., when a moving ice cover stops and thickens. The water variables
tend to respond slower and smoother. One would expect that the results obtained
from the loosely coupled and fully coupled models would approach each other as
the time step is reduced. A program listing for UNCTHK is also included in Zufelt
and Ettema (1996).
The remainder of this section demonstrates the capabilities of the model THKFUL
with sample output plots for a "baseline" configuration of geometric, hydraulic,
and ice characteristics. The robustness of the calculation technique is demonstrated
and the results of sensitivity testing with relation to Courant number and theta
weighting factors for the water and ice are presented. Alternate boundary condi-
tions are described and the effects of using variable size length steps are addressed.
Baseline runs
A baseline configuration was developed to provide a standard against which
future runs could be compared. Care was taken in developing this 5-km-long
"hypothetical river" to make sure that the geometric, hydraulic, and ice character
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