A viscous free surface flow solver using the Spectral Element Method

Abstract

A viscous free surface flow solver is introduced in this paper. The present model of the fluid motion is based on the Navier-Stokes equations of velocity-pressure formulation. In order to deal with the free surface motion, an Arbitrary Lagrangian-Eulerian (ALE) description is adopted. The governing equations are solved through the Spectral Element Method (SEM), which possesses the property of highorder spatial accuracy as proposed by Karniadakis & Sherwin (2005). The solution procedure and characteristic aspects of the present modeling and numerical method are briefly addressed. The essential part of the present method is focused upon the treatment of kinematic and dynamic free surface boundary conditions. It is shown that the proposed SEM and its present implementation produce very accurate and convergent solutions to several test problems including manufactured one of N-S equations. Numerical results of the lid-driven cavity flow are also compared with other numerical results. As for the viscous free surface flows, viscous sloshing with a prescribed initial free surface profile and run-up of soliton on vertical wall are simulated to check the accuracy of the present method. Generation of nonlinear free-surface waves by applying pressure distribution on some portion of the free surface is realized in our numerical wave flume. Copyright ？ 2008 by The International Society of Offshore and Polar Engineers (ISOPE).