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Numerical simulation of unsteady viscous free surface flow. (English) Zbl 0701.76036
Summary: A finite element method is presented for the numerical simulation of time-dependent incompressible viscous free surface flows. The time- dependent primitive equations are solved sequentially using explicit time marching procedure. The method is based on a velocity correction approach to the time integration of the Navier-Stokes equations in which only the incompressibility condition is treated implicitly. A special arbitrary mixed Lagrangian-Eulerian description has been used to avoid the typical problems encountered in a purely Lagrangian description. The method appears applicable for small computers; problems requiring several thousand nodes can be solved on personal computers. Numerical experiments have been performed that show that this approach is reasonably efficient and robust for a range of complicated highly nonlinear problems.

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
76M10 Finite element methods applied to problems in fluid mechanics
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76D33 Waves for incompressible viscous fluids
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