Transient free surface flows via a stabilized ALE finite element method

J. Schmidt, W. A. Wall, E. Ramm

Research output: Contribution to journalArticlepeer-review


Free surface problems appear in a wide range of industrial and engineering applications, e.g. when modelling sloshing of fluid in a container or when tracking the free surface evolution in casting and molding processes. A finite element technique is presented to study time-dependent large free surface motions of viscous, incompressible fluids. The approach is based upon an arbitrary Lagrangean-Eulerian (ALE) representation of kinematics and field equations, i.e. continuum mechanical conservation laws. Both convective effects and equal-order interpolation for velocities and pressure are stabilized in a Galerkin least-squares sense. This leads to a fully stabilized finite element method (FEM) for the governing instationary incompressible Navier-Stokes equations. The algorithmic setup is complemented by a combination of the stabilized FEM with direct time integration procedures and fixed point-like iterative schemes. The performance of the overall algorithm is demonstrated with the help of selected two-dimensional numerical examples.

Original languageEnglish
Pages (from-to)S547-S548
JournalZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Issue number4 SUPPL. 2
StatePublished - 2000
Externally publishedYes


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