A flow of Bingham-Il'yushin viscoplastic medium in plane channels of varying width is studied numerically, based on the variational formulation. The effect of the domain geometry and yield stress on the shape, size and location of rigid regions is studied. The earlier unknown qualitative characteristics of flows are described. The problem of stopping viscoplastic medium flows in pipes of various cross-sections is numerically investigated. The numerical analyses revealed a peculiar characteristic, namely, the appearance of stagnant zones during cessation that partly or completely, depending on the cross-section, surround the boundary contour.
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