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

236 Shallow-water problems
Fig. 7.12 Supercritical ¯ow and formation of shockwaves in symmetric channel of variable width contours of
h. In¯ow Froude number ˆ 2.5. Constriction: 158.
7.5 Drying areas
A special problem encountered in transient, tidal, computations is that of boundary
change due to changes of water elevation. This has been ignored in the calculation
presented for the Bristol Channel±Severn Estuary as the movements of the
boundary are reasonably small in the scale analysed. However, in that example
these may be of the order of 1 km and in tidal motions near Mont St. Michel,
France, can reach 12 km. Clearly on some occasions such movements need to be
considered in the analysis and many di€erent procedures for dealing with the
problem has been suggested. In Fig. 7.13 we show the simplest of these which is
e€ective if the total movement can be con®ned to one element size. Here the
boundary nodes are repositioned along the normal direction as required by elevation
changes .
If the variations are larger than those that can be absorbed in a single element some
alternatives can be adopted, such as partial remeshing over layers surrounding the
distorted elements or a general smooth displacement of the mesh.