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 incompressible, viscous, nonhomogeneous (variable density) fluid. By computing the flow fields in both the liquid and gas regions in a consistent manner, the free surface can be captured as a discontinuity in the density field, thereby eliminating the need for special free surface tracking procedures. The numerical algorithm is developed using a conservative, implicit, finite volume discretization of the equations of motion. The algorithm incorporates the artificial compressibility method in conjunction with a dual time-stepping strategy to maintain a divergence-free velocity field. A slope-limited, high-order MUSCL scheme is adopted for approximating the inviscid flux terms, while the viscous fluxes are centrally differenced. The capabilities of the surface capturing method are demonstrated by calculating solutions to several two- and three-dimensional problems.

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