THE DEVELOPMENT OF A FREE-SURFACE CAPTURING APPROACH FOR MULTIDIMENSIONAL FREE-SURFACE FLOWS IN CLOSED CONTAINERS

A new surface-capturing method is developed for numerically simulating viscous free surface flows in partially filled containers. The method is based on the idea that the flow of two immiscible fluids within a closed container is governed by the equations of motion for an incompr essible, viscous, nonhomogeneous (variable density) fluid. By computin g the how fields in both the liquid and gas regions in a consistent ma nner, the free surface can be captured as a discontinuity in the densi ty field, thereby eliminating the need for special free surface tracki ng procedures. The numerical algorithm is developed using a conservati ve, implicit, finite volume discretization of the equations of motion. The algorithm incorporates the artificial compressibility method in c onjunction with a dual time-stepping strategy to maintain a divergence -free velocity field. A slope-limited, high-order MUSCL scheme is adop ted for approximating the inviscid flux terms, while the viscous fluxe s are centrally differenced. The capabilities of the surface capturing method are demonstrated by calculating solutions to several two-and t hree-dimensional problems. (C) 1997 Academic Press.