@article {11995,
title = {A two-dimensional vertical non-hydrostatic sigma model with an implicit method for free-surface flows},
journal = {International Journal for Numerical Methods in Fluids},
volume = {44},
number = {8},
year = {2004},
pages = {811-835},
abstract = {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{\textendash}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 {\textcopyright} 2004 John Wiley \& Sons, Ltd.},
isbn = {731971TL2166},
doi = {10.1002/fld.670},
url = {http://onlinelibrary.wiley.com/doi/10.1002/fld.670/full},
author = {Yuan, H.L. and Chin H. Wu}
}