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<br />Momentum <br />dU au <br />-- + u.- + <br />dt ax <br /> <br />d ah aao <br />v a~ + g-dX + g--ax - <br /> <br />1/2 <br />+ ~ (u2 + v2) <br />Ch <br /> <br />Cxx d2U c~ a2u <br />--Pax:! - p'OyL - 2",vsin ~ <br /> <br />a_v + uav + av ah <br />v-+g--+ <br />dt ax ay ay <br />1j2 <br />+9L (u2 + v2) _ <br />CZh <br /> <br />.1;.. V2 cos lJ! ~ 0 ( 2) <br />h a <br />aao Sf_x. a2v Sf.x.a2v + 2",u sin <P <br />g--- - ax7 - p '07 <br />ay p <br /> ,. <br />.z;.. V 2 ( 3) <br />h a sin lj; = 0 <br /> <br />where <br />u. v = x and y velocity componl?nts respectively <br />t = time <br />h = depth <br />ac= bed elevation <br />c = turbulent exchange ~oefficients <br />9 = gravitational acceleration <br />w = rate of earth's angular rotation <br /><p = latitude <br />C = Chezy roughness coefficient <br />, = empirical wind stress coefficient <br />Va= wind speed <br />lj; = angle between wind direction and x axis <br />p = fluid density <br /> <br />Before solution, the equations are recast with flow (velocity <br />times depth) and depth as the dependent variables. A linear <br />shape function is used for depth and a quadratic function for <br />flow. The Galerkin method of weighted residuals is used and <br />the resulting non-linear system of equations solved with the <br />Newton-Rapheson scheme. Details of the solution have been <br />published previously by Norton, et al (1973) and King, et al <br />(1975). General discussions of finite element techniques have <br />been published by Zienkiewicz (1971). Hubner (1975), and Strang <br />& Fix (1973). <br /> <br />Evaluation of ContinuitLJ.r:.rors <br />The finite element method yields a solution which approximates <br />the true solution to the governing partial differential <br />equations. The approximate nature of this solution becomes <br />evident when mass continuity is checked at various locations <br />in the solution domain for a steady state simulation. Although <br />overall continuity is maintained (inflow equals outflow over <br />the boundary). calculated flows across int~rnal sections <br />deviate some\'lhat from the inflow/outflow values. A study was <br />made to evaluate errors in continuity as a function of network <br />density. Poor continuity approximation is important of itself <br />if water quality simulation is the goal. In the present <br />applications. however. water surface elevations and velocities <br />are the variables of intel-est. Therefore. the impact of <br /> <br />-? <br />