"Application of a complete multi-network method for solving the problem of flows around sphere "
DOI:
https://doi.org/10.31489/2019No1/69-72Keywords:
numerical solution, multigrid method, viscosity, flow, sphere, ellipsoidAbstract
Using the example of a numerical solution of the classical problem of a viscous flow past a sphere, the efficiency of using the multigrid method was compared with direct calculations. Various difference schemes are considered. It's shown that to go from grid to grid, for a vortex equation, it is necessary to use a 9-point pattern. For different Reynolds numbers the resistance coefficient to friction had been calculated. The limit on the Reynolds number when using the multigrid method is noted.
References
"1 Fletcher C. Computational Techniques for Fluid Dynamics. Moscow, Mir. 1991, Vol. 1, 504 p. [in Russian]
Jenson V. G. Viscous flow round a sphere at low Reynolds (<40). Proc. Roy. Soc. London, Ser. A, 1959, Vol. 249, № 1258, p. 346-366.
Roache P.J. Computational hydrodynamics. Moscow, Mir. 1980, 616 p. [in Russian]
Lamb G. Hydrodynamics. Moscow, Gostekhizdat. 1947, 928 p. [in Russian]
Happel D., Brenner G. Hydrodynamics at lоw Reynolds numbers. Moscow, Mir. 1976, 630 p. [in Russian]
Dudin I.V., Narimanov R.K. Resistance of a triaxial ellipsoid slowly moving in a viscous fluid. Preprint №37, TSU publishing house, Tomsk, 2000, 11 p. [in Russian]
Dudin I.V., Narimanov R.K. Resistance in slow movement of the ellipsoid. Proceedings of the Tomsk Polytechnic University, Tomsk, 2004, Vol. 307, No.3, pp. 17-21. [In Russian]
Dudin I.V., Narimanov R.K., Narimanova G.N. Resistance moment at rotation of an ellipsoid in viscous fluid. Eurasian Physical Technical Journal. 2018, Vol. 15, No. 2(30), pp. 40-48.
Zamyshlyaev A. A., Shrager G. R. Fluid Flows past Spheroids at Moderate Reynolds Numbers. Fluid Dynamics, Vol. 39, No. 3, 2004, pp. 376–383
Lipanov A.M., Semakin A.N. Non-spherical particles: resistance and some flow parameters in unlimited volume. Scientific notes TsAGI. 2011, Vol. XLII, No. 6, pp. 15 – 22. [in Russian]
Holser A., Sommerfeld M. New simple correlation formula for the drag coefficient of non-spherical particles. Powder Technology. 2008, Vol.184, Issue 3, pp. 361 – 365.
Loth E. Drag of non-spherical solid particles of regular and irregular shape. Powder Technology, 2008, Vol. 182, Issue 3, pp. 342 – 353.
Clift R., Grace J.R., Weber M. Bubbles, drops and particles. New York, Academic press, 1978, 380p.
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