ИСТИНА

We solve numerically start-up and cessation of plane and circular Couette flow and plane and axisymmetric (both for circular and annular pipes) Poiseuille flow of Bingham medium. The resolution of the corresponding variational inequalities describing the flows is based on the iterative Uzawa-like method. We use finite-difference scheme in space and implicit (backward Euler) scheme in time. The calculated stopping times in all examined cases are just below the theoretical upper bounds provided by Glowinski & Huilgol et al. for the whole range of Bingham numbers. The applied algorithm allows easy determination of the yielded and unyielded regions thus we present evolution of rigid zones during considered unsteady flows. In the recent papers by Chatzimina et al. The very interesting effect was noted: an appearance of dead zone near the wall during the cessation of the axisymmetric Poiseuille flow for one of Bingham numbers. The results obtained show that this effect takes place for various Bingham numbers in circular pipes a nd also in annular pipes with small ratio. Besides, we find the same effect for circular Couette flow. We also present results for the more complicated screw motion.