Finite element simulation of two- and three-dimensional free surface flows. (English) Zbl 0761.76037

Summary: This paper is devoted to the free surface flow finite elements simulation. Arbitrary Lagrangian (or referential) kinematic description is used in order to express the conservation equations in a moving domain. The geometrical nonlinearities are found to be expressed analytically into the conservation equations and into the corresponding variational model, thus with simple linearization of the referential motion one obtains the appropriate approximated variational model. The numerical procedures developed and the finite element implementations are discussed and assessed numerically by some two- and three-dimensional benchmark examples.


76M10 Finite element methods applied to problems in fluid mechanics
76M30 Variational methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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