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A time splitting projection scheme for compressible two-phase flows. Application to the interaction of bubbles with ultrasound waves

Huber, Grégory and Tanguy, Sébastien and Béra, Jean-Christophe and Gilles, Bruno A time splitting projection scheme for compressible two-phase flows. Application to the interaction of bubbles with ultrasound waves. (2015) Journal of Computational Physics, 302. 439-468. ISSN 0021-9991

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Official URL: http://dx.doi.org/10.1016/j.jcp.2015.09.019


This paper is focused on the numerical simulation of the interaction of an ultrasound wave with a bubble. Our interest is to develop a fully compressible solver in the two phases and to account for surface tension effects. As the volume oscillation of the bubble occurs in a low Mach number regime, a specific care must be paid to the effectiveness of the numerical method which is chosen to solve the compressible Euler equations. Three different numerical solvers, an explicit HLLC (Harten–Lax–van Leer-Contact) solver [48], a preconditioning explicit HLLC solver [14] and the compressible projection method , and , are described and assessed with a one dimensional spherical benchmark. From this preliminary test, we can conclude that the compressible projection method outclasses the other two, whether the spatial accuracy or the time step stability are considered. Multidimensional numerical simulations are next performed. As a basic implementation of the surface tension leads to strong spurious currents and numerical instabilities, a specific velocity/pressure time splitting is proposed to overcome this issue. Numerical evidences of the efficiency of this new numerical scheme are provided, since both the accuracy and the stability of the overall algorithm are enhanced if this new time splitting is used. Finally, the numerical simulation of the interaction of a moving and deformable bubble with a plane wave is presented in order to bring out the ability of the new method in a more complex situation.

Item Type:Article
Additional Information:Thanks to Elsevier editor. The definitive version is available at http://www.sciencedirect.com The original PDF of the article can be found at http://www.sciencedirect.com/science/article/pii/S0021999115006129
HAL Id:hal-01315405
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
French research institutions > Institut National de la Santé et de la Recherche Médicale - INSERM (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Other partners > Université Claude Bernard-Lyon I - UCBL (FRANCE)
Laboratory name:
Deposited On:13 May 2016 08:37

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