Zienkiewicz O.C., Taylor R.L. Vol. 3. The finite - tiera.ru

The region studied was approximately 55 kilometres long and the mean value of the
eddy di€usivity was of k ˆ 40 m s ÿ1 . The limiting time step for convection (considering
eight components of tides) was 3.9 s. This limit was severely reduced to 0.1 s if the
di€usion term was active and solved explicitly. The convective limit was recovered
assuming an implicit solution with 3 ˆ 0:5. The comparisons of di€usion error
between computations with 0.1 s and 3.9 s had a maximum di€usion error of 3.2%
for the 3.9 s calculation, showing enough accuracy for engineering purposes, taking
into account that the time stepping was increased 40 times, reducing dramatically
the cost of computation. This reduction is fundamental when, in practical applications,
the behaviour of the transported quantity must be computed for long-term
periods, as was this problem, where the evolution of the salinity needed to be
calculated for more than 60 periods of equivalent M 2 tides and for very di€erent
initial conditions.
In Fig. 7.14 we show by way of an example the dispersion of a continuous hot water
discharge in an area of the Severn Estuary. Here we note not only the convection
movement but also the di€usion of the temperature contours.
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