5. Engineering applications

b. The experimental results of the dam-break on a dry bed channel with varying width are used to examine numerical models [16]. The laboratory measurements of flow parameters for the dam-break in the nonprismatic converging-diverging channel are

c. The so-called right-angled open channel junction test gives a complex twodimensional flow structure which is highly inhomogeneous in the cross section of the main channel [43]. Such a kind of comparison with essentially 2D currents is an

d. The dam-break flow over a triangular obstacle contains a large number of characteristic features [38], including the downstream over the dry channel bed, the smooth rarefaction wave, the upstream reflected shock, and the downstream shock after passing the triangular obstacle. The formation of a reflected shock wave from the boundary wall passing back through the hump causes complex nonlinear oscillations

e. An analytical solution for steady flow case with spatially varying width, bed, and friction slope of special kind is known [38, 44]. There is a singular point in the flow in the transition from the inclined profile to the shallow bottom. A fine structure of the

f. The use of various software, for example, FLOW-3D, FLOW-3D-SWM, MIS2D, is a fast and effective way for the verification of new numerical models of shallow water [45].

Figure 6 shows the results of the numerical simulations of shear flow instability (Kelvin-Helmholtz instability) in shallow water using the CSPH-TVD method. The characteristic stages

Figure 6. The problem of the tangential velocity discontinuity is represented by: (a) the time dependence of the minimum (shown by solid line) and maximum (shown by dashed line) of the amplitude of the water depth disturbances Hw(t) = H (t) H<sup>0</sup> (H<sup>0</sup> H(0)); (b) the spatial distribution of the vorticity of the velocity vector field ω = ∇ v/2 at t = 110. The dashed

solution in the vicinity of this point is a good test for numerical models.

important stage in testing of the numerical model [16].

described in Ref. [38].

248 Numerical Simulations in Engineering and Science

in such a basin.

line shown the position of the tangential discontinuity.

We have developed software to solve some engineering applications utilizing the parallel implementation of the CSPH-TVD method on GPUs.

