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<br />2.5 <br /> <br />where 1'1 is Manning's roughness coefficient, No viscous or intern~ shear <br />stress terms are considered in resistance s'lope equation as presented in <br />Equations 2.6 and 2.7. The model represented by Equations 2.1, 2.5, 2.6, and <br />2.7 in two dimensions is inappropriate for high concentrations of sediment flow. <br />A di scuss i on of the modifications for hyperconcentrated sediment flow appears <br />in the following sections. <br />Wave attenuation in the diffusive model is the result of the interaction <br />of the friction slope and diffusive pressure gradient terms with the bed slope. <br />It shoul d be made cl ear that the MUDFLOW mode I does not have the abi I ity to s i mu. <br />late shock waves or hydraulic jumps and tends to smooth out these abrupt chan, <br />ges in the flow profile. Also, the model assumes a rigid boundary, and does not $ <br />simulate the transient phenomena of surging or channel avulsion, <br /> <br />2.3 Numerical Scheme for Clear-Water Flows <br />The numeri ca 1 approximat i on of the cont i nuity and momentum equat ions, <br />referred to as nodal domain integration (ND!) methods (Hromadka et al., 1985), <br />employs a finite difference technique to solve the linear equations using uniform <br />grid elements. The net water volume and the change in the depth of water are <br />computed assuming a linear trial function (coverage depth) between nodal points. <br />The model advances in time using an explicit method <br /> <br />11 i + 1 = AH i + Hi <br />c c c <br /> <br />(2.8) <br /> <br />in which c denotes the center nodal point of the four surrounding grids for <br />time steps i and i+l with a At time step interval. Each cell'centered node <br />is equal to a function of the four neighboring cell nodal points. The solution <br />algorithm takes the following steps: <br /> <br />1. The flow is discretized by uniform nodal points, each possessing a unique <br />roughness value, elevation, and initial flow depth (zero on the alluvial <br />fan). <br /> <br />2. Average geometry and Manni ng' s 1'1 rou~Jhness val ue are computed between <br />nodal points. <br /> <br />3, The flow depth for the nodal poi nt be i ng exami ned is I!St i mated for the <br />next time step and evaluated expl icitly using a combined form of the <br />diffusive wave and continuity equations, <br />