Summary
We examine plane inertial flows of viscoelastic fluids with an instantaneous elastic response. In such flows, the vorticity equation can change type when the velocity of the fluid exceeds the speed of shear waves. We use a finite element algorithm which has been developed for calculating highly viscoelastic flows.
The algorithm is tested for supercritical flow regimes on the problem of the flow through a wavy channel. We next consider the problem of the flow of a Maxwell fluid around a circular cylinder for various flow regimes. We compare creeping flows, Newtonian flows and supercritical viscoelastic flows. We show that the flow kinematics is affected by supercritical flow conditions. In particular, a vorticity shock forms ahead of the cylindrical body.
The work of V. Delvaux is supported by the “Service de Programmation de la Politique Scientifique”.
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V. Delvaux and M.J. Crochet, in preparation.
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Crochet, M.J., Delvaux, V. (1990). Numerical Simulation of Inertial Viscoelastic Flow with Change of Type. In: Keyfitz, B.L., Shearer, M. (eds) Nonlinear Evolution Equations That Change Type. The IMA Volumes in Mathematics and Its Applications, vol 27. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9049-7_4
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DOI: https://doi.org/10.1007/978-1-4613-9049-7_4
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