Efficient solving method for unsteady incompressible interfacial flow problems

Abstract

Unsteady interfacial problems, considered in an Eulerian form, are studied. The phenomena are modeled using the incompressible viscous Navier–Stokes equations to get the velocity field and an advection equation to predict interface evolutions. The momentum equation is solved by means of an implicit hybrid augmented Lagrangian–Projection method, whereas an explicit characteristic method coupled with a TVD SUPERBEE scheme is applied to the advection equation. The velocity components and the pressure are discretized on staggered grids with finite volumes. Emphasis is on the accuracy and robustness of the techniques described before. A precise explanation on the validation phase will be given, which uses such tests as the advection of a step function or Zalesak's problem to improve the calculation of the interface. The global approach is used on a physically hard interfacial test with strong disparities between viscosities and densities. Copyright © 1999 John Wiley & Sons, Ltd.