Direct boundary element simulations of 3D bubble dynamics in potential and Stokes flows

Yulia Itkulova, Olga Abramova, Nail Gumerov

Objective:

Application of boundary element method to study different effects in bubbly liquids

Bubble dynamics in a potential flow

The boundary element method (BEM) is a numerical method for solving partial differential equations, which can be represented in the boundary integral form. Concerning numerical solution of micro- and nanoscale dynamics of dispersed systems problems in a number of cases the BEM is more efficient than other methods. This is due to the fact that this method enables to reduce the problem dimensionality by one as only the domain boundaries and interfaces are discretized.

Bubble dynamics in a Stokes flow

Two mathematical models and program modules for bubble dynamics simulations at low and high Reynolds numbers are developed and implemented. So, two extreme cases are considered, first, when the influence of inertia is neglected, and, second, when the viscosity is neglected. The BEM is selected as a numerical basis for Stokes and potential flows since it is very effectient for 3D bubble dynamics. The direct method of calculation of matrix-vector product on graphics processors (GPU) or the Fast Multipole Method (FMM) implemented on heterogeneous architectures (many-core CPU and GPU) are used to accelerate the BEM and, hence, to increase the problem size. These accelerations enable direct simulations of 3D dynamics of a single bubble, two interacting bubbles with high surface discretizations, or a bubble cluster containing a large amount of bubbles. The developed approach can be used to solve a wide range of problems of Stokes and potential flows of bubbly liquids.

Prospects:

The developed method can be used to study the 3D dynamics of free and forced bubble shape oscillations