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<br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I, <br />I <br />I <br />I <br />I <br />I <br />I <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 />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 />and each may have curved sides. Integration in space is performed by Gaussian integration <br /> <br />and derivatives in time are replaced by a non-linear finite difference approximation. Solutions <br /> <br /> <br />are fully implicit and the set of simultaneous equations is solved by Newton-Raphson non- <br /> <br /> <br />linear iteration. RMA2 permits wetting and drying within the grid either through elemental <br /> <br /> <br />elimination or gradual wetting and drying through the consideration of marsh porosity (King <br />1997) <br /> <br />Modeling low flow conditions over a long reach of river has proven problematic for <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 />the element. Once an element "dries", flow must get around the newly formed land boundary <br /> <br />until the projected depth exceeds a specified value for all nodes ofthe 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 />disconnected from the main body of flow, RMA2 is likely to diverge when the pond is <br />reattached to the wetted network. <br /> <br />25 <br />