ИСТИНА

Many viscoplastic fluids slip at the wall with a yield slip. The fluid slips when the tangential stress exceeds a critical value called the yield slip, and otherwise, the fluid sticks at the wall. We exploit the analogy of structure between the slip law and the viscoplastic constitutive law and apply accelerated proximal gradient method to both the viscoplastic model and the yield slip equation. The traditional ALM converges with rate O(1/ √ k), an accelerated variant converges with the higher and provably optimal bound O(1/k) convergence, where k is the iteration counter. This accelerated version is obtained at a negligible extra computational cost. The proposed method is used to simulate the axisymmetric squeeze flow of Bingham, Casson, and Herschel-Bulkley fluids with the slip yield boundary condition at the wall. The squeeze flow has shown three specific behaviors: stick, stick-slip transition, and slip. As a second example of the application of this algorithm, the Poiseuille flow of a Bingham fluid in ducts of various cross sections with slip yield boundary condition is considered. There exist five flow regimes: full slip, full stick, partial slip and stick at the wall, block translation, and stopped materia