Труды Института механики им. Р.Р. Мавлютова

ISSN 2542–0380

Электронный научный журнал | Electronic Scientific Journal

Proceedings of the Mavlyutov Institute of Mechanics

Butyugina E.V., Nasibullaeva E.Sh., Akhatov I.Sh., Gumerov N.A. Conservative Scheme Application for the Numerical Modeling of the Diffusion Problem for a Single Bubble in an Acoustic Field Proceedings of the Mavlyutov Institute of Mechanics. 10 (2014). 32–37.

2014. Vol. 10. Issue 1, Pp. 32–37
URL: http://proc.uimech.org/uim2014.1.006,en
DOI: 10.21662/uim2014.1.006

Conservative Scheme Application for the Numerical Modeling of the Diffusion Problem for a Single Bubble in an Acoustic Field

Butyugina E.V.^∗,∗∗, Nasibullaeva E.Sh.^∗, Akhatov I.Sh.^{∗∗,∗∗∗}, Gumerov N.A.^{∗∗,∗∗∗∗}

^∗ Mavlyutov Institute of Mechanics, Ufa
^∗∗ Center for Micro and Nanoscale Dynamics of Dispersed Systems, Bashkir State University, Ufa
^∗∗∗ Department of Mechanical Engineering, North Dakota State University
^∗∗∗∗ Institute for Advanced Computer Studies University of Maryland, College Park, Maryland

Abstract

In the present study a numerical method for simulation of the diffusion problem for a single gas bubble oscillating in an acoustic field is developed. The method is based on the conservative numerical scheme for the diffusion equation where diffusion flux continuity is acting as conservation law. This method allows one to take into account the influence of changing mass of the gas inside the bubble on the strongly nonlinear dynamics of a bubble. The numerical results obtained using the proposed method utilizing conservative scheme and the standard scheme, which does not conserve the total mass of the gas-liquid system, reveals that in the latter case the numerical error may accumulate and lead to physically incorrect results.