American Society of Civil Engineers


A Fully Non-hydrostatic Three-Dimensional Model with an Implicit Algorithm for Free-Surface Flows


by Chin H. Wu, (Department of Civil and Environmental Engineering, University of Wisconsin, Madison) and Hengliang Yuan, (Department of Civil and Environmental Engineering, University of Wisconsin, Madison)
Section: Model Structure, pp. 591-607, (doi:  http://dx.doi.org/10.1061/40734(145)37)

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Document type: Conference Proceeding Paper
Part of: Estuarine and Coastal Modeling (2003)
Abstract: A three-dimensional (3D) implicit numerical model based upon the Navier-Stokes equations (NSE) for free-surface flows is developed. To avoid solving the fully 3D Pressure Poisson Equation (PPE), an algorithm is developed by decoupling the original matrix system into a series of sub-matrix systems corresponding to two-dimensional (2D) vertical planes. The features of the model include (1) a novel treatment for the non-hydrostatic pressure at the top-layer cell in a staggered grid, consistent with the overall non-hydrostatic pressure discretization; (2) the option of partial-cell treatment on bottom topographies, enabling the model to simulate free-surface flows interacting with uneven bottoms with a reasonable vertical resolution; (3) simultaneously solving all flow-field components (e.g., the velocities, pressure, and free-surface elevation) within each time step; and (4) capability of simulating both 3D short waves and long waves with a second-order accuracy in both time and space. The developed model is validated by two free-surface flow problems, in which the vertical accelerations are considerable and thus the pressure fields are in non-hydrostatic distributions. The numerical results are in excellent agreements with the analytical solutions and experimental data, illustrating the capability of the algorithm for simulating 3D free surface flows.


ASCE Subject Headings:
Hydrostatics
Three-dimensional models
Free surfaces
Water flow