FLOW AROUND A CYLINDER - istiarto

– 5.12 –
� The two test runs, Test A and B, achieve a near perfect agreement between the
computed and measured velocity distributions. In Test A, the logarithmic velocity
distribution prevails along the channel. In Test B the development of the velocity
profile, from a uniform distribution to the logarithmic one, is achieved after half reach
of the computational domain. The agreement between this computed velocity profile
and the measured one has confirmed that the wall boundary treatment is appropriately
implemented in the model.
� The computed eddy-viscosity profile compares favorably with the measured one. The
eddy viscosity is zero at the surface, increases with the depth until a maximum value
at around mid-depth, and decreases towards zero at the bed.
� The computed shear-stress profiles in Test A and B well agree with the
measurements. The shear stress is linearly distributed with the depth, being zero at the
surface and maximum at the bed.
Computational history of the model variables
Having obtained a good agreement with the experimental data, the evolution of the flow
variables during the iterative computation of the model is investigated. This evolution of
flow variables, as the computation marches towards the steady-state solution, is plotted in
Fig. 5.5, Fig. 5.6, and Fig. 5.7 for Tests A, B, and C, respectively. Shown are some
selected flow variables (z surface , p, u, k, and �) at 5 computational nodes (inlet and outlet
boundary cells, and at x/L = 0.25, 0.5, 0.75). The plots show that stable computations
towards the converged solution are observed in all test runs.
The computational history plots of Test A and B (see Fig. 5.5 and Fig. 5.6), however,
reveal an interesting behavior of the iteration (the � or m iteration, see Chapter 4) in the
model. These figures clearly show that the iterations are devoted almost uniquely to the
pressure computation. When the velocity and the k-� have already converged, i.e. their
values have no longer changed appreciably, the pressure is still changing. This leads to a
conclusion that the pressure convergence criterion in the �-iteration may be loosened.
However, since the pressure is used as the basis for the water surface computation, this
strategy would endanger the stability of the latter. To circumvent this problem, two
c
≤
different criteria are used for the pressure convergence. The first criterion is loose ( pmax c
10 [Pa], which is equivalent to pmax c c
much smaller ( pmax≤ 0.01 [Pa] or pmax
� ≤ 1 [mm]) for the �-iteration and the second one is
� ≤ 0.001 [mm]) for the water surface
computation. Consequently, the water surface may not be necessarily updated every time
step.
With the above strategy, the run of Test B was repeated in Test C. It was found that the
final result of Test C does not show a significant difference from that of Test B. The
computational history in these two test runs, of course, is not the same. Fig. 5.7 depicts
the computational history of certain variables in Test C; this is to be compared to that of
Test B, Fig. 5.6. Compared to Test B, the computation in Test C, as expected, converges