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<br />The front of the negati ve wave propagating into the still water in <br />the reservoir defines the upstream boundary of the flow field where con- <br />ditions are the same as the undisturbed initial conditions. Upstream <br />boundary conditions are determined in this fashion until about the <br />negative wave front reaches the upstream reservoir end at time tE given <br />by <br /> <br />. <br /> <br />tE = 2Fo IM+r <br /> <br />(8) <br /> <br />, <br /> <br />Shortly before that time, when a depth smaller than a prescribed depth Ym <br />is obtained at the moving upstream boundary, a fictitious stream of the <br />same depth is introduced at the ultimate location of the upstream boundary <br />and assumed existing thereafter. The velocity is determined using the <br />backward characteristic relation. Typical values of Ym are: Ym = 0.01 <br />for Fo ~ 0.5 and Ym = 0.03 for Fo = 0.025. <br /> <br />In the region very close to the wave tip where y+O and dY/dx + -~ <br />the formal numerical solution is very costly to apply. Instead, the water <br />surface profile is determined analytically usinG a simplified form of Eq. <br />4b suggested by Whitham (7) and based on physical considerations of the <br />tip region. Typical values of y up to which the formal computation proceeds <br />are in the order of 0.04. <br /> <br />Solution of EqS. 4 yield values of depth and velocity at the nodes <br />of the characteristics grid in the x-t plane. Data pertaining to stage <br />and discharge hydrographs at various locations along the channel are <br />obtained through linear interpolation between node values. <br /> <br />, <br /> <br />4 <br />