By Weiming Wu
This complete textual content at the basics of modeling circulation and sediment shipping in rivers treats either the actual rules and numerical equipment for numerous levels of complexity. It covers 1-D, 2-D (both intensity- and width-averaged), and 3-D versions, in addition to the combination and coupling of those versions. the amount features a wide choice of numerical tools for open-channel flows, similar to the SIMPLE(C) algorithms on staggered and non-staggered grids, the projection procedure, and the circulation functionality and vorticity technique. the various labored examples illustrate numerous stipulations, similar to reservoir sedimentation, channel erosion because of dam development, and channel widening and meandering.
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105). However, if C is defined by Eq. 100), a dispersion term should appear in Eq. 106). Normally, the diffusion term in Eq. 108) Integrating Eq. 109) where ∂Ab /∂t is the rate of change in bed area; Ab is the cross-sectional area of the bed above a reference datum, as shown in Fig. 7; Aδ is the cross-sectional area of the bed-load zone; Qb is the bed-load transport rate at the cross-section; and Cδ is the laterally-averaged bed-load concentration. In analogy to Eq. 90), by using Cδ = Qb /(Aδ Ub ), Eq.
The modiﬁed k and ε equations are still formulated as Eqs. 25Pk /ε. 15. , 1997). Yakhot et al. (1992) rederived the ε equation using the renormalized group (RNG) theory. One new term was introduced to take into account the highly anisotropic features of turbulence, usually associated with regions of large shear, and to modify the viscosity accordingly. This term was claimed to improve the simulation accuracy of the RNG k-ε turbulence model for highly strained flows. 42 − η(1 − η/η0 )/(1 + βη3 ).
Armanini and di Silvio’s function, Eq. 017 is also plotted in Fig. 8. It is shown that for small Rouse numbers Eq. 135) is close to Zhou and Lin’s curve for deposition case, and as the Rouse number increases, the difference between Eqs. 136) increases. It is also shown that the values of α given by these two methods are always larger than 1. It should be noted that Eqs. 136) were derived for a pure vertical 2-D case under many assumptions and simplifications. 3. 3 Complexity of adaptation coeff icient of sediment Effect of cross-sectional shape The value of α in the 1-D model is related to the cross-sectional shape.