Table of Contents
ISRN Applied Mathematics
Volume 2012, Article ID 451693, 15 pages
Research Article

The Analytical Expression for the Mass Flux in the Wet/Dry Areas Method

School of Earth and Environment, Centre for Computational Fluid Dynamics, University of Leeds, Leeds LS2 9JT, UK

Received 31 July 2012; Accepted 23 August 2012

Academic Editors: M. F. El-Sayed and L. You

Copyright © 2012 Xianyun Wen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Accurate prediction of the distribution of shear stress is essential for the numerical investigation of the interaction between the wind and water waves on ocean surface since the shear stress plays a key role in this type of interfacial flows. The numerical velocity distribution provided by the computational fluid dynamics should have high accuracy as the shear stress is computed by the derivative of the numerically predicted velocity. The recently developed wet/dry areas method based on the conservative integral form of the Navier-Stokes equations mathematically reveals that the convection terms in the Navier-Stokes equations should be calculated by the areas exposed to the water and air. In this paper, an analytical expression for the mass flux in the wet/dry areas method is derived, the discussion is focused on why this analytical expression should be used for more accurate numerical simulation of interfacial (free surface) flows.