%0 Journal Article
%J International Journal for Numerical Methods in Fluids
%D 2004
%T A two-dimensional vertical non-hydrostatic sigma model with an implicit method for free-surface flows
%A Yuan, H.L.
%A Chin H. Wu
%X An implicit finite difference model in the σ co-ordinate system is developed for non-hydrostatic, two-dimensional vertical plane free-surface flows. To accurately simulate interaction of free-surface flows with uneven bottoms, the unsteady Navier–Stokes equations and the free-surface boundary condition are solved simultaneously in a regular transformed σ domain using a fully implicit method in two steps. First, the vertical velocity and pressure are expressed as functions of horizontal velocity. Second, substituting these relationship into the horizontal momentum equation provides a block tri-diagonal matrix system with the unknown of horizontal velocity, which can be solved by a direct matrix solver without iteration. A new treatment of non-hydrostatic pressure condition at the top-layer cell is developed and found to be important for resolving the phase of wave propagation. Additional terms introduced by the σ co-ordinate transformation are discretized appropriately in order to obtain accurate and stable numerical results. The developed model has been validated by several tests involving free-surface flows with strong vertical accelerations and non-linear waves interacting with uneven bottoms. Comparisons among numerical results, analytical solutions and experimental data show the capability of the model to simulate free-surface flow problems. Copyright © 2004 John Wiley & Sons, Ltd.
%B International Journal for Numerical Methods in Fluids
%V 44
%P 811-835
%@ 731971TL2166
%G eng
%U http://onlinelibrary.wiley.com/doi/10.1002/fld.670/full
%R 10.1002/fld.670