Geodesic
Solving the problem of Bingham fluid flow in cylindrical pipeline
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2015), pp. 82-86

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We consider an elliptic variational inequality in a circular domain, which simulates viscoplastic Bingham flow in a pipe. This variational inequality is approximated by finite-difference scheme on a grid in polar coordinates. To solve the finite-dimensional problem we propose a generalized Uzawa-type iterative method. We prove the convergence of the iterative method.
Keywords: Bingham's flow, finite-difference approximation, iterative method. 
@article{IVM_2015_2_a9,
     author = {A. V. Lapin and A. D. Romanenko},
     title = {Solving the problem of {Bingham} fluid flow in cylindrical pipeline},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {82--86},
     publisher = {mathdoc},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_2_a9/}
}
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A. V. Lapin; A. D. Romanenko. Solving the problem of Bingham fluid flow in cylindrical pipeline. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2015), pp. 82-86. http://geodesic.mathdoc.fr/item/IVM_2015_2_a9/