Abstract
A three-dimensional boundary-element method is proposed for the numerical simulation of confined free surface flow problems. Although the method is applicable to viscous and inviscid flows, the present formulation will be limited to potential flow, including transient and nonlinear waves in cavities of general shape. The emphasis in this study, however, will be on the flow driven by a plunger in cylindrical cavities, typically as it arises in the shot sleeve of a die casting machine. Unlike most existing (two-dimensional) Lagrangian formulations, the present method is based on a mixed Eulerian–Lagrangian formulation whereby the partially filled cavity is discretized into volume elements that deform along and with the plunger movement. The fluid, at any time, occupies part of the cavity, and the domain of computation thus changes as the fluid flows within the cavity. At each time step, the solution is obtained using boundary element discretization and an explicit (Euler) time stepping scheme. Numerical results will be given for both rectangular and cylindrical cavities.
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