ИСТИНА

The Duvaut-Lions variational inequality is considered as a mathematical model of the Bingham medium. We propose two finite-difference schemes which are generalisations of schemes on staggered and semi-staggered grids. A special stabilizing term which allows using in 3D case is introduced for the second scheme. For the time-discretization, we used the standard backward-Euler scheme. At each time step, the nonlinear system of discretized equations was solved by using the Uzawa-like iterative method. The numerical modeling of the unsteady cavity flows (start-up and cessation) and Poiseuille flows of viscoplastic medium in channels of different cross-sections is presented. The results obtained are consistent with theoretical bounds.