Improvement of Non-Hydrostatic Hydrodynamic Solution Using a Novel Free-Surface Boundary Condition

Abstract

Hydrodynamic models based on the RANS equation are well-established tools to simulate three-dimensional free surface flows in large aquatic ecosystems. However, when the ratio of vertical to horizontal motion scales is not small, a non-hydrostatic approximation is needed to represent these processes accurately. Increasing efforts have been made to improve the efficiency of non-hydrostatic hydrodynamic models, but these improvements require higher implementation and computational costs. In this paper, we proposed a novel free-surface boundary condition based on a fictional sublayer at the free-surface (FSFS). We applied the FSFS approach at a finite difference numerical discretization with a fractional step framework, which uses a Neumann type of boundary condition to apply a hydrostatic relation in the top layer. To evaluate the model performance, we compared the Classic Boundary Condition Approach (CBA) and the FSFS approach using two numerical experiments. The experiments tested the model’s phase error, capability in solving wave celerity and simulate non-linear wave propagation under different vertical resolution scenarios. Our results showed that the FSFS approach had a lower phase error (2 to 5 times smaller) than CBA with a little additional computational cost (ca. 7% higher). Moreover, it can better represent wave celerity and frequency dispersion with 2 times fewer layers and low mean computational cost (CBA $\delta$ t = 2.62 s and FSFS $\delta$ t = 1.22 s).