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<br />r ; <br /> <br />x,y, t cartesian coordinates and time <br />p = density of fluid <br />E eddy viscosity. coefficient <br />for xx = normal direction on x axis surface <br />for yy = normal direction on y axis surface <br />for xy and yx = shear direction on each surface <br />g = acceleration due to gravity <br />a = elevation at bottom <br />n = Mannings roughness coefficient <br /> <br />rOO; <br /> <br />Equations 3,4, and 5 .are solved by the finite.element method using the. Galerkin <br /> <br />Method of weighted residuals. Elements may be two dimensional quadrilaterals or triangles <br /> <br />F1 <br />lJ <br /> <br />and each may have curved sides. Integration in space is performed by Gaussian integration <br /> <br />n <br />u <br /> <br />and derivatives in time are replaced by a non-linear finite difference approximation. Solutions <br /> <br />are fully implicit and the set of simultaneous equations is solved by Newton-Raphson non- <br /> <br />f'-l <br />I <br /> <br />linear iteration. RMA2 permits wetting and drying within the grid either ~hrough elemental <br /> <br />elimination or gradual wetting and drying through the consideration of marsh porosity (King <br /> <br />1997) <br /> <br />L1 <br />U <br /> <br />Modeling low flow conditions over a long reach of river has proven problematic for <br /> <br />~~ <br /> <br />many reasons including the need for a highly refined finite element mesh and a large amount <br /> <br />of computing power. The elemental elimination method for wetting and drying removes <br /> <br />elements as soon as the water surface elevation drops below the elevation of anyone node on <br /> <br />~...:....'...:1: <br />.~.:J <br />.:.~., <br /> <br />the element. Once an element "dries", flow must get around the newly formed land boundary <br /> <br />p <br />,.~ <br />L j <br /> <br />until the projected depth exceeds a specified value for all nodes of the element. If the <br /> <br />elements are large, the change in velocities in the remaining areas can be large enough to <br /> <br />cause the solution to diverge and the model to crash. Additionally, if an element becomes <br /> <br />~, J <br />, e <br />r , <br />U <br /> <br />disconnected from the main body of flow, RMA2 is likely to diverge when the pond is <br /> <br />reattached to the wetted network. <br /> <br />[1 <br />\': ,lI <br /> <br />1-_ _1 <br /> <br />25 <br />