An implicit method for slow-moving free-surface boundary of open channel flows

Abstract

This paper outlines the implementation of an efficient implicit method for a free surface boundary for solving free surface flows with larger time steps. In this method, the governing equations are solved with dynamic conditions applied to the free surface boundary. The position and shape of the free surface are represented with adaptive boundary grid points. Unlike existing explicit methods, the proposed method solves the space conservation equation implicitly, making the calculations more stable and at a lower computational cost. The approach was implemented numerically by developing a new boundary field in OpenFOAM. Several test cases, including propagations of tidal wave, channel surge and solitary wave, were simulated to demonstrate the method’s accuracy. The proposed method accurately predicted the first two cases using larger time steps. The Courant number of the solitary wave case should be less than 1 to reduce numerical errors, which would damp the wave amplitude.