Geodesic
Uzawa algorithm implementation for steady incompressible Newtonian liquids
Journal of computational and engineering mathematics, Tome 1 (2014) no. 2, pp. 26-31.

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In this article Uzawa algorithm for steady incompressible Newtonian liquids was implemented. The flow model of these liquids is described by Navier – Stokes equation. Uzawa method involves the Delaunay triangulation of a set and computation of values in the middle of every triangle's edge. The method is iterative and the proper implicit scheme that describes the flow of an incompressibe Newtonian liquid is introduced. For the computational experiment the centrifuge model was taken. The abstract example is about stiring the incompressible Newtonian liquid inside the centrifuge. The result of the computational experiment corresponds to practise: the pressure increase towards the wall, the lowest pressure is in the middle. The results of this research will be helpful for the further research of steady incompressible non-Newtonian liquids in the same condition.
Keywords: mathematical physics equations, partial differential equations, Newtonian fluid, Uzawa algorithm. 
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A. V. Belov; S. Roper. Uzawa algorithm implementation for steady incompressible Newtonian liquids. Journal of computational and engineering mathematics, Tome 1 (2014) no. 2, pp. 26-31. http://geodesic.mathdoc.fr/item/JCEM_2014_1_2_a2/

[1] C. Truesdell, W. Noll, The Non-Linear Field Theories of Mechanics, Springer-Verlag, Berlin, 2004, xxx+602 pp. | DOI | MR

[2] K. R. Rajagopal, “On Boundary Conditions for Fluids of the Differential Type”, Navier – Stokes Equations and Related Nonlinear Problems, Springer US, New York, 1995, 273–278 | DOI | MR

[3] K. R. Rajagopal, P. N. Kaloni, “Some Remarks on Boundary Conditions for Flows of Fluids of the differential type”, Continuum Mechanics and its Applications, Hemisphere, New York, 1989, 935–942 | MR

[4] R. S. Rivlin, J.L. Ericksen, “Stress-deformation relations for isotropic materials”, J. Rational Mech. Anal., 4 (1955), 323–425 | DOI | MR | Zbl

[5] R. Temam, Navier – Stokes Equations, North Holland Press, Amsterdam – New York, 1979, xvi+454 pp. | MR | Zbl

[6] K. Arrow, L. Hurwicz, H. Uzawa, Studies in Linear and Non-Linear Programming, Stanford University Press, Stanford, 1958, 229 pp. | MR | Zbl