Geodesic
Determination of the line separating domains of vortical flows
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 1 (2013), pp. 3-10 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the framework of Lavrentiev–Shabat's model of separated flows a vorticity area under ideal fluid flow in a circular chamber with a ledge is proved and numerically simulated. The work has direct application to the study of the kinematic pattern of velocity distribution in bypass galleries of lock chambers. Fluid flow in a circular chamber is of vortex character, presence of a ledge leads to another area of vortex flow. The problem of gluing (pairing) of two vortex flows is a generalization of Goldshtik problem of separated vortex flows in areas with potential flow. We prove the existence of solution of generalized Goldshtik problem. The proposed proof essentially uses potential theory. The method of proof is based on approximation of problem solutions with discontinuous nonlinearity by discontinuous solutions of linear problems of Poisson equation type. The possibility of approximating by linear problems is used in the numerical implementation. In the second part of the paper the zone of flow separation in a circular chamber with a ledge is numerically simulated. The results obtained from numerical simulation are compatible with experimental measurements. Bibliogr. 9. Il. 4.
Keywords: ideal fluid flow, fluid with constant vorticity, harmonic functions, Dirichlet problem. 
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A. V. Vasin. Determination of the line separating domains of vortical flows. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 1 (2013), pp. 3-10. http://geodesic.mathdoc.fr/item/VSPUI_2013_1_a0/

[1] Lavrent'ev M. A., Shabat B. V., Problemy gidrodinamiki i ih matematicheskie modeli (Problems of hydrodynamics and their mathematical models), Nauka, Moscow, 1977, 408 pp. | MR

[2] Gol'dshtik M. A., Vihrevye potoki (Vortex flows), Nauka, Novosibirsk, 1981, 366 pp.

[3] Potapov D. K., “O reshenijah zadachi Gol'dshtika (On solutions of Goldshtik problem)”, Sib. zhurn. vychisl. matematiki, 15:4 (2012), 409–415 | MR

[4] Vajnshtejn I. I., “Reshenie dvuh dual'nyh zadach o sklejke vihrevyh i potencial'nyh techenij variacionnym metodom M. A. Gol'dshtika (The decision of the two dual problems of matching the vortex and potential flows by variational method of M. A. Goldshtik”, Zhurn. Sib. Federal. un-ta. Ser. Matematika i fizika, 4:3 (2011), 320–331

[5] Vajnshtejn I. I., Jurovskij V. K., “Ob odnoj zadache soprjazhenija vihrevyh techenij ideal'noj zhidkosti (A problem of vortex pairing ideal fluid flows)”, Zhurn. prikl. mehaniki i tehn. fiziki, 1976, no. 5, 98–100

[6] Potapov D. K., “Matematicheskaja model' otryvnyh techenij neszhimaemoj zhidkosti (Mathematical model of separated flow of incompressible fluid)”, Izv. RAEN. Ser. MMMIU, 8:3–4 (2004), 163–170

[7] Potapov D. K., “Nepreryvnye approksimacii zadachi Gol'dshtika (Continuous approximation of the Goldshtik problem)”, Matem. zametki, 87:2 (2010), 262–266 | MR | Zbl

[8] Potapov D. K., “Bifurkacionnye zadachi dlja uravnenij jellipticheskogo tipa s razryvnymi nelinejnostjami (Bifurcation problems for elliptic equations with discontinuous nonlinearities)”, Matem. zametki, 90:2 (2011), 280–284 | MR | Zbl

[9] Vasin A. V., Timofeeva O. A., “Opredelenie linii razdela oblastej s potencial'nym i vihrevym techenijami (Determination of the line separating the areas with the potential and vortex flows)”, Zhurn. Un-ta vodnyh kommunikacij, 2012, no. 2, 8–13 | MR