An Efficient Boundary Fitted Non-Hydrostatic Model for Free-Surface Flows

Abstract

A boundary fitted non-hydrostatic finite volume model is presented to simulate two dimensional vertical free surface flows effectively deploying only 2-4 vertical layers. The algorithm is based on a projection method which results in a block tri-diagonal system of equation with pressure as the unknown. This system can be solved by a direct matrix solver without iteration. To purpose of minimise the computational cost, a new top-layer pressure treatment is proposed which enables the model to simulate relatively short wave motion with very small vertical layers accurately. The test of linear and nonlinear sinusoidal short wave propagation with significant vertical accelerations is applied correctly using a small number of layers.