Geoscience Reference
In-Depth Information
V P
C n + 1
sa , P
C sa , P ) =
a W C n + 1
sa , W
a E C n + 1
sa , E
a S C n + 1
sa , S
a N C n + 1
sa , N
a B C n + 1
sa , B
t (
+
+
+
+
a T C n + 1
sa , T
a P C n + 1
sa , P
+
+
S sa
(12.42)
where
A b are the areas of cell faces t and b projected on the horizontal
plane, respectively; and J Tsw , t and J Bsw , t are the short-wave radiations penetrating to
the water surface and reflected from the bottom surface, respectively.
It should be noted that the finite volume method and finite difference method han-
dle the surface heat fluxes differently. In the finite volume method, when integrating
Eq. (12.4) over the control volume near the water surface shown in Fig. 4.22, the
long-wave radiation and latent and sensible heat fluxes are specified directly at t -
face and arranged into the source term, and then the coefficient a T is set to be
zero. In the finite difference method, Eq. (12.36) is often used to determine the
temperature at the water surface. However, Eq. (12.36) has been reported to be
inefficient. More recently, many finite difference models also arrange the surface
heat fluxes into the source term, following the approach used in the finite volume
method.
Because flow density is influenced by temperature and salinity, the above heat and
salinity transport equations should be solved with the flow model in a coupled form.
For example, the SIMPLE algorithm for the full 3-D hydrodynamic model is described
below:
A t and
(1) Guess the salinity, temperature, and pressure p ;
(2) Calculate the flow density
ρ using the state equation (12.12);
(3) Solve the momentum equations to obtain u i ;
(4) Solve the p equation (7.14);
(5) Calculate p n + 1 by adding p to p ;
(6) Calculate u n + i using the velocity-correction relation (7.9) and the intercell fluxes
using Eqs. (7.10)-(7.12);
(7) Solve the transport equations (12.41) and (12.42);
(8) Treat the corrected pressure p as a new guessed p , and repeat the procedure from
step 2 to 6 until a converged solution is obtained;
(9) Calculate other water quality constituents, if needed; and
(10) Conduct the calculation of next time step if the unsteady flow is concerned.
Nevertheless, in the well-mixed cases, the effects of temperature and salinity on the
flow are often neglected so that the hydrodynamic model may be decoupled from the
computations of heat and salinity transport.
12.2 WATER QUALITY MODEL
Pollutants from municipal and industrial wastes (point sources) and from agricultural
fields, urban and suburban runoff, groundwater and atmosphere (nonpoint sources)
significantly affect the water quality in aquatic systems. They may be conservative or
non-conservative, transport through convection and diffusion, and transform through
 
 
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