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Direct simulation of fluid particle motions. (English) Zbl 0754.76054

The authors develop a package that simulates the unsteady two-dimensional solid-liquid two-phase flows using the Navier-Stokes equations for the liquid and Newton’s equations of motion for the solid particles. The former are solved through a finite-element formulation and the latter through an explicit-implicit scheme. The authors show that the simplest fully explicit scheme to update the particle motion using Newton’s equations is unstable. To correct this instability they propose and implement the explicit-implicit scheme in which, at each time step, the positions of the particles are updated explicitly, the computational domain is remeshed, the solution at the previous time is mapped onto the new mesh and the Navier-Stokes equations and the discretized Newton’s equations are solved iteratively on the new mesh. The procedure is illustrated through its application to sedimentation of one and two discs (cylinders) in a vertical two-dimensional channel of finite width, and it is shown that it is able to reproduce successfully the effects of the vortex shedding on the motions of the cylinders and the drafting-kissing and tumbling scenario which is dominant in two-dimensional beds of spheres.
Reviewer: D.Jou (Ballaterra)

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76T99 Multiphase and multicomponent flows
76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena
76D05 Navier-Stokes equations for incompressible viscous fluids
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References:

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