Finite Element Modeling in Free-Surface Hydromechanicsby A. J. Baker, Univ of Tennessee, United States,
G. S. Iannelli, Univ of Tennessee, United States,
Abstract: A finite element semi-discrete approximation is applied to the conservation law form of the two-dimensional, depth-averaged free-surface Navier-Stokes equations governing incompressible flows. The issues of accuracy, stability and false diffusion are addressed theoretically using a weak statement formed on a temporal Taylor series augmentation to the conservation law statement. The resultant algorithm is implemented using bilinear finite elements, an implicit time integration and an efficient split matrix iteration procedure. Numerical results document performance for pertinent hydromechanical flow geometries.
Subject Headings: Finite element method | Navier-Stokes equations | Free surfaces | Mathematical models | Hydrologic models | Free flow | Water flow | Two-dimensional flow
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