A. M. Bubenchikov, V. A. Korobitsyn, D. V. Korobitsyn, P. P. Kotov, Yu. I. Shokin, “Numerical simulation of multiply connected axisymmetric discontinuous incompressible potential flows”, Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 7,Pages <nobr>1194

Numerical simulation of multiply connected axisymmetric discontinuous incompressible potential flows

A. M. Bubenchikov^a, V. A. Korobitsyn^a, D. V. Korobitsyn^b, P. P. Kotov^a, Yu. I. Shokin^c

^a Tomsk State University, pr. Lenina 36, Tomsk, 634050, Russia
^b Tomsk State University of Control Systems and Radio Electronics, pr. Lenina 40, Tomsk, 634050, Russia
^c Institute of Computational Technologies, Siberian Branch, Russian Academy of Sciences, Novosibirsk, pr. Akademika Lavrent’eva 6, 630090, Russia

Abstract: The ascend and evolution of an axisymmetric gas bubble are studied numerically using an inviscid incompressible potential flow model. The volume of the gas bubble varies adiabatically. The transition from a simply connected bubble to a doubly connected toroidal one and its interaction with the free surface are simulated. The change in connectedness is accompanied by a nonzero velocity circulation and a discontinuous velocity potential occurring over an arbitrary toroidal liquid surface enclosing the bubble.

Key words: incompressible fluid, free surface, toroidal bubble, change in connectedness, circulation, discontinuity of velocity potential, axial symmetry, numerical simulation, Laplace’s equation.

UDC: 519.634

MSC: 76T10

Received: 28.11.2011
Revised: 24.09.2012

DOI: 10.7868/S0044466914070059