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Stability of superposed viscous - viscoelastic (couple-stress) fluids in the presence of variable magnetic field through porous medium

Kumar P., Sharma P.

International Journal of Applied Mechanics and Engineering

2008

Vol. 13, no 3

837-845

The Rayleigh-Taylor instability of a Newtonian viscous fluid overlying a couple-stress viscoelastic fluid through a porous medium is considered in the presence of a variable horizontal magnetic field. The stability analysis is carried out, for mathematical simplicity, for two highly viscous fluids of equal kinematic viscosities. For the stable configuration, the system is found to be stable or unstable under certain conditions. However, for the unstable configuration, the magnetic field has got stabilizing effects.

A Lagrangian Finite Element Treatment of Transient Gravitational Waves in Compressible Viscous Fluids

Staroszczyk R.

Archives of Hydro-Engineering and Environmental Mechanics

2007

Vol. 54, nr 4

261-284

In this paper the problem of transient gravitational wave propagation in a viscous compressible fluid is investigated. The problem is formulated in the Lagrangian description and is solved numerically by a finite element method. In computations either fixed in space or moving meshes that follow the material fluid particles are used with the purpose to compare their numerical performance. As illustrations, results of numerical simulations carried out for plane flows in a domain of simple geometry are presented. First, the finite element results are compared with available experimental data for the case of small-amplitude waves in order to validate the numerical model. Then, the problem of large-amplitude transient water wave propagation over a horizontal bottom, involving the wave reflection at a rigid wall, is considered. For the flow parameters typical of a laboratory flume, the evolution of the free-surface elevation and the time variations of the surface displacements at chosen locations are shown for a range of different moving wall amplitudes and excitation times.