The development of a free surface capturing approach for multidimensional free surface flows in closed containers. (English) Zbl 0903.76058

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. 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, higher-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.


76M20 Finite difference methods applied to problems in fluid mechanics
76B55 Internal waves for incompressible inviscid fluids
76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
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