 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| L.V. Muravleva and E.A. Muravleva, "Bingham-Il'yushin Viscoplastic Medium Flows in Channels with Undulating Walls," Mech. Solids. 46 (1), 47-51 (2011) |
| Year |
2011 |
Volume |
46 |
Number |
1 |
Pages |
47-51 |
| DOI |
10.3103/S0025654411010079 |
| Title |
Bingham-Il'yushin Viscoplastic Medium Flows in Channels with Undulating Walls |
| Author(s) |
L.V. Muravleva (Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991 Russia, lvmurav@gmail.com)
E.A. Muravleva (Institute of Numerical Mathematics, Russian Academy of Sciences, Gubkina 8, Moscow, 119333 Russia, catmurav@gmail.com) |
| Abstract |
In the present paper, the flow of a Bingham-Il'yushin viscoplastic medium in plane channels with undulating walls is studied numerically. The influence of the region geometry and the yield point on the shape, dimensions, and location of rigid regions are studied. The obtained results are compared with the results of other authors who also used the thin layer approximation. The earlier unknown qualitative characteristics of flows are noted. |
| Keywords |
Bingham-Il'yushin viscoplastic medium, variable width channels, variational inequalities, numerical methods |
| References |
| 1. | A. A. Il'yushin,
"Deformation of a Viscoplastic Body,"
Uch. Zap. MGU. Mekh.,
No. 39 (1940). |
| 2. | D. M. Klimov, A. G. Petrov, and D. V. Georgievskii,
Viscoplastic Flows: Dynamic Chaos, Stability, Mixing
(Nauka, Moscow, 2005)
[in Russian]. |
| 3. | O. B. Magomedov and B. E. Pobedrya,
"Certain Problems of Viscoelastoplastic Flow,"
in Elasticity and Non-Elasticity, No. 4
(Izd-vo MGU, Moscow, 1975),
pp. 152-169
[in Russian]. |
| 4. | R. V. Goldstein and V. M. Entov,
Qualitative Methods in Continuum Mechanics
(Nauka, Moscow, 1989; Wiley, New York, 1994). |
| 5. | L. V. Muravleva and E. A. Muravleva,
"Unsteady Flows of a Viscoplastic Medium in Channels,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 164-188 (2009)
[Mech. Solids (Engl. Transl.)
44 (5), 792-812 (2009)]. |
| 6. | L. Muravleva, E. Muravleva, G. C. Georgiou, and E. Mitsoulis,
"Numerical Simulation of Cessation flows of Bingham Plastic
with the Augmented Lagrangian Method,"
J. Non-Newton. Fluid Mech.
165 (9-10), 544-550 (2010). |
| 7. | V. I. Vishnyakov, K. B. Pavlov, and A. S. Romanov,
"Peristaltic Flow of a Non-Newtonian Viscoplastic Liquid in a Slot Channel,"
Inzh. Fiz. Zh.
31 (3), 499-505 (1976)
[J. Engng Phys. Themophys. (Engl. Transl.)
31 (3), 1078-1082 (1976)]. |
| 8. | A. V. Gnoevoi, D. M. Klimov, and V. M. Chesnokov,
Foundations of the Theory of Flows of Bingham Media
(Fizmatlit, Moscow, 2004)
[in Russian]. |
| 9. | R. Glowinski, J. L. Lions, and R. Trémolieres,
Numerical Analysis for Variational Inequalities
(Dunod, Paris, 1976; Mir, Moscow, 1979; North Holland, Amsterdam, 1981). |
| 10. | L. V. Muravleva and E. A. Muravleva,
"Uzawa Algorithm on Semi-Staggered Grids for Unsteady Bingham Media Flows,"
Russ. J. Num. Anal. Math. Model.
24 (6), 543-563 (2009). |
| 11. | I. A. Frigaard and D. Ryan,
"Flow of a Visco-Plastic Fluid in a Channel of Slowly Varying Width,"
J. Non-Newton. Fluid Mech.
123, 67-83 (2004). |
| 12. | A. Putz, I. A. Frigaard, and D. M. Martinez,
"On the Lubrication Paradox and the Use of Regularization Methods for Lubrication Flows,"
J. Non-Newton. Fluid Mech.
163, 62-77 (2009). |
|
| Received |
10 October 2010 |
| Link to Fulltext |
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