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<br />4 <br /> <br />DEVELOPMENT OF GENERALIZED FREE SURFACE FLOW l,jODElS <br />USING FINITE ELEMENT TECHNIQUES <br /> <br />D. Michael Gee, Robert C. MacArthur <br /> <br />The Hydrologic Engineering Center, U.S. Army COt'PS of <br />Engineers, Davis, Cal ifornia <br /> <br />INTRODUCTION <br /> <br />The Corps of Engineers' Hydrologic Engineering Center is <br />involved in the development, evaluation, and application of <br />mathematical models. Two finite element hydrodynamic models, <br />one for two-dimensional free surface flow in the horizontal <br />plane and one for the vertica1 plane are being evaluated. <br />Although the rnodels are fonnulated to solve dynamic flow <br />problems, all work to date has been with steady state solutions. <br />Recent research has focused on mass continuity performance of <br />the models, proper boundary cO'1dition specification, and <br />comparison with finite difference techniques. The objective <br />of this research is to develop generalized lI;athematical models <br />for routine use by the engineering community. This paper <br />presents recent results of evaluation and application of the <br />models. <br /> <br />THE MODEL FOR HIO-DIMENSIONAl FREE SURFACE FLOW IN THE <br />HORIZONTAL PLANE <br /> <br />The model for t\'/o-dimensional free surface flow in the <br />horizontal plane solves the governing equations in the <br />fo 11 owi ng fonn: <br /> <br />c <br /> <br />Conti nuity <br />ah a a ( 0 <br />'if + ax (uh) + 'ay vh) = <br /> <br />(1) <br /> <br />; <br />