A New Approach to Three-Dimensional Free-Surface Flow Modeling

by Jan J. Leendertse


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This report describes an efficient model for the computation of three-dimensional free-surface flows. For the time integration, two different approximations are used in succession. The advection term approximations depend on the flow direction and introduce stability into the computation. The gradients of the advection terms are generally computed directly, whereas the coefficients of the nonlinear terms must be computed by iteration. Experiments show that only two iterations are required. The finite difference approximations used in the computation are of the second order, and no time filtering or introduction of viscosity is required for stability. The timestep is limited by the accuracy desired in the results. In the formulation, it is assumed that the pressures are hydrostatic. A stability analysis that uses linearized coefficients in the nonlinear terms indicates that the computation method is unconditionally stable. To investigate the effect of different timesteps on model results, the author made several experiments that confirmed the analysis of the behavior of the computation method showing that the growth of disturbances with small wavelength and periods is inhibited. A model of a lake (IJsselmeer) showed that, with limited computer resources, effective three-dimensional flow and transport computations can be made.

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