Abstract
AbstractFree surface problems appear in a wide range of industrial and engineering applications, e.g. when modeling 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.
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Schedule a callMore From: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
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