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<br />160 Computational Fluid Dynamic.< <br /> <br />I Hereford e/l/I.. 19'! I. 1993; Thompson and Potochnik, 20(1)) may have been offset in <br />the pre-dam era by the inlilling and healing of incipient gullies by windblown sand. <br />The mechanism linking channel-side sand deposits with the erosion of upslope <br />artefacts is uncertain and likely to be the subject of ongoing inve>ligation. Never. <br />theless. [he mechanisms described above provide motivation for evaluating the <br />volume and locations of sand deposition in response to sand supplies and dam <br />releases beyond the simple sand-storage concerns that have dominated past sand <br />>Iudies in Grand Canyon. Short of experimenting with a variety of high flo\\'s. which <br />is not feasible and would in any case run the risk of permanently damaging cultural <br />resources. the best option is the application of a model that has been demonstrated <br />10 represent well the complex flow. sand transport, and erosion and deposition <br />patterns in previous studies. <br /> <br />. <br /> <br />14.2 Flow and sediment transport model <br /> <br />14.2.1 Model <br /> <br />The numerical methods used in the model are described by Wiele e/<1I. (1996) and are <br />based on Patankars finite volume method (I9~0), which features a staggered grid <br />and upwind differencing 10 solve the Ihree equations of motion for the vertically <br />averaged. 2D now liold. A key attribute of the linite volume method is that it <br />consc;:rves mass. a crucial requirement for sediment transport applications. The flow <br />algorithms must contend with cl)mple\ now lields. typically induding recirculation <br />zones. which generate strong velocity gradients. A diffusion-advection equation is <br />used to calculate the 3D sand concentration field from which the local suspended <br />sand transport can be determined. A turbulence closure is applied to recover the <br />vertical structure of the turbulent mixing and Ihe velocity prolile. Local bedload also <br />is calculated on the basis of local shear stress 3t the bed. critical shear stress and local <br />bed slope. The change in bed conliguralion over a small lime step is calculated from <br />the divergence of the 10lal sand transport rale. <br />The now field is calculaled by numerically solving the momentum equations in the <br />downstream direction, <br /> <br />. <br /> <br />(II (II au (j C-II C au (th + 'I s) T,. 0 <br />-;::;-+II:;-+lI:::---=:-E---::-~-+g ----::---- +-= <br />CI ex e..v ex ax OJ CX e,x ph <br /> <br />(14.1) <br /> <br />and cross-stream direction. <br /> <br />ev (1/ (,v C (v (, (.u eh"", Tl <br />-:;-+V-TU-;;;---~--::::-~:;:--:-g----;;;;--T-=O (14.2) <br />e/ 0.1' cx By C.1' ex e,x . ey ph <br /> <br />and wilh Ihe continuity equation <br /> <br />eh ~ cllh + tvh = 0 <br />c/ 'ex or <br /> <br />, 1~.3' <br /> <br />- <br /> <br />. <br />