Total volume conservation in simulation of unsteady free-surface flows

Abstract

Free surface tracking methods used in the numerical simulation of unsteady free surface flows may-introduce sources or sinks resulting in changes in total fluid volume in the computational domain. A com­putational model is developed for incompressible, 2-dimensional, unsteady free surface flows to investigate the conditions of total volume conservation. The model is based on finite volume discretization of the Navier-Stokes equations coupling momentum and mass conservation. Free surface position is tracked using a depth-integrated continuity equation. Possible free surface cell configurations and a solution procedure for continuity are described. A flux-corrected transport method is applied to the free surface solution to main­tain numerical stability and eliminate unphysical surface oscillations. The discretization scheme and the computer code are validated in lid-driven cavity flow. Liquid sloshing in a partially filled rectangular tank and dam-break flows are simulated. Numerical solutions preserving total volume are presented. Computed free surface profiles are verified by experimental data.