Simulation of bubble dynamics in three-dimensional potential flows on heterogeneous computing systems using the fast multipole and boundary element methods


  • Yu.A. Itkulova Bashkir State University
  • O.A. Abramova Bashkir State University
  • N.A. Gumerov University of Maryland
  • I.Sh. Akhatov University of North Dakota


bubble dynamics, potential flow, boundary element method, fast multipole method, parallel computing, graphics processors


The bubble dynamics in potential flows of incompressible liquid is studied. The proposed approach is based on the boundary element method for the Laplace equation, which is especially efficient for the 3D bubble dynamics. In order to increase the problem size and to accelerate computations, an efficient numerical algorithm is developed and implemented. Depending on the problem size, for the acceleration of computations we used the direct matrix-vector multiplication on graphics processors (GPU) or the fast multipole method (FMM) implemented on heterogeneous computing systems (multicore CPUs and graphics processors). For the simulation of bubble surfaces, a new method based on the filtration of spherical harmonics is proposed. The proposed approach allows one to directly calculate the 3D dynamics of a single bubble, two and three interacting bubbles as well as a bubble cluster with a high degree of surface discretization. The developed method can be used to solve a wide range of problems related to the potential flow of bubble liquids.

Author Biographies

Yu.A. Itkulova

Bashkir State University
• Research Intern

O.A. Abramova

Bashkir State University
• Junior Researcher

N.A. Gumerov

University of Maryland, Baltimore,
620 W. Lexington St., Baltimore, MD 2120, USA
• Professor

I.Sh. Akhatov

University of North Dakota,
Faculty of Mechanical Engineering
• Professor


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How to Cite

Иткулова Ю.А., Абрамова О.А., Гумеров Н.А., Ахатов И.Ш. Simulation of Bubble Dynamics in Three-Dimensional Potential Flows on Heterogeneous Computing Systems Using the Fast Multipole and Boundary Element Methods // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2014. 15. 239-257



Section 1. Numerical methods and applications