"Simulation of bubble dynamics in three-dimensional potential flows on heterogeneous computing systems using the fast multipole and boundary element methods"
Itkulova Yu.A., Abramova O.A., Gumerov N.A., and Akhatov I.Sh.

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.

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

  • Itkulova Yu.A. – Bashkir State University, Center for Micro- and Nanoscale Dynamics of Dispersed Systems; ulitsa Zaki Validi 32, Ufa, 450076, Russia; Trainee Researcher, e-mail: Itkulova.Yulia@bashedu.ru
  • Abramova O.A. – Bashkir State University, Center for Micro- and Nanoscale Dynamics of Dispersed Systems; ulitsa Zaki Validi 32, Ufa, 450076, Russia; Junior Scientist, e-mail: abramovacmndds@gmail.com
  • Gumerov N.A. – University of Maryland, Institute of Advanced Computer Studies; Room 3305, A.V. Williams Building, College Park, USA, MD 20742; Professor, e-mail: gumerov@umiacs.umd.edu
  • Akhatov I.Sh. – North Dakota State University, Department of Mechanical Engineering; NDSU Dept 2490, 210 Dolve Hall, P.O. Box 6050, Fargo, USA, ND 58108; Professor, e-mail: Iskander.Akhatov@ndsu.edu