Lagrangian finite‐element analysis of time‐dependent viscous free‐surface flow using an automatic remeshing technique: Application to metal casting flow

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Abstract
The Navier‐Stokes incompressible model is used to describe two‐dimensional metal casting flow. Such flows involve moving free boundaries. A new numerical algorithm has been developed using the Lagrangian finite‐element method. It allows treatment of flows with moderate Reynolds numbers. The main feature is to avoid the calculation of the convective term, together with an automatic remeshing technique, to cure the mesh distortions. The problem of the free oscillation of a liquid is treated to verify the formulation. An application of this method to the computation of an industrial metal casting flow situation is presented.