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An arbitrary Lagrangian-Eulerian finite element method for solving three-dimensional free surface flows. (English) Zbl 0948.76043
Summary: This paper discusses numerical solution of unsteady three-dimensional free surface flows. The governing equilibrium equations are written in the framework of the arbitrary Lagrangian-Eulerian kinematic description. The corresponding variational formulation is established afterwards. Since the variational problems are nonlinear with respect to the moving coordinates, we derive a second-order approximate variational problem after a consistent linearization of the referential motion. Stability of the discrete formulations is ensured with the help of a new stabilization method. A robust preconditioned GMRES algorithm is then used to solve the resulting set of nonlinear equations. Finally, the computational algorithms are assessed through numerical studies of various problems: a large sloshing flow in a three-dimensional reservoir, a discharge flow from a reservoir, simulation of a liquid vortex produced inside a cylindrical container with a disk rotating at the bottom, and a three-dimensional practical hydraulic problem.

76M10 Finite element methods applied to problems in fluid mechanics
76B07 Free-surface potential flows for incompressible inviscid fluids
76B47 Vortex flows for incompressible inviscid fluids
76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
Full Text: DOI
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