Olga A. Abramova

High-Performance BEM Simulation of 3D Emulsion Flow

Direct simulations of the dynamics of a large number of deformable droplets are necessary for a more accurate prediction of rheological properties and the microstructure of liquid-liquid systems that arise in a wide range of industrial applications, such as enhanced oil recovery, advanced material processing, and biotechnology. The present study is dedicated to the development of efficient computational methods and tools for understanding the behavior of three dimensional emulsion flows in Stokes regime. The numerical approach is based on the accelerated boundary element method (BEM) both via an efficient scalable algorithm, the fast multipole method (FMM), and via the utilization of advanced hardware, particularly, heterogeneous computing architecture (multicore CPUs and graphics processors). Example computations are conducted for 3D dynamics of systems of tens of thousands of deformable drops and several droplets with very high discretization of the interface in shear flow. The results of simulations and details of the method and accuracy/performance of the algorithm are discussed. The developed approach can be used for the solution of a wide range of problems related to emulsion flows in micro- and nanoscales.

An efficient method for simulation of the dynamics of a large number of deformable droplets in the stokes regime

Direct simulations of the interaction of a large number of deformable droplets are necessary for more accurate predictions of rheological properties and the microstructure of liquid-liquid systems. In the present study, a mathematical model of a three-dimensional flow of a mixture of two Newtonian liquids of a droplet structure in an unbounded domain at low Reynolds numbers is considered. An efficient computational method for simulation of the dynamics of a large number of deformable drops is developed and tested. This approach is based on the boundary element method for three-dimensional problems accelerated both via an advanced scalable algorithm (FMM), and via utilization of a heterogeneous computing architecture (multicore CPUs and graphics processors). This enables direct simulations of systems of tens of thousands of deformable droplets on PCs, which is confirmed by test and demo computations. The developed method can be used for solution of a wide range of problems related to the emulsion flow in micro- and nanoscales. Also it can be used to establish the closing relations for simulation of two-phase liquid-liquid flow based on the continuum approach in macroscales.

BEM-based numerical study of three-dimensional compressible bubble dynamics in stokes flow

The dynamics of compressible gas bubbles in a viscous shear flow and an acoustic field at low Reynolds numbers is studied. The numerical approach is based on the boundary element method (BEM), which is effective as applied to the three-dimensional simulation of bubble deformation. However, the application of the conventional BEM to compressible bubble dynamics faces difficulties caused by the degeneration of the resulting algebraic system. Additional relations based on the Lorentz reciprocity principle are used to cope with this problem. Test computations of the dynamics of a single bubble and bubble clusters in acoustic fields and shear flows are presented.

FMM/GPU Accelerated BEM Simulations of Emulsion Flow in Microchannels

Modeling of motion of two-phase liquids in microchannels of different shape is needed for a variety of industrial applications, such as enhanced oil recovery, advanced material processing, and biotechnology. Development of efficient computational techniques is required for understanding the mechanisms of many effects in “liquid-liquid” systems, such as the jamming of emulsion flows in microchannels and blood cell motion in capillaries. In the present study, a mathematical model of a three-dimensional flow of a mixture of two Newtonian liquids of a droplet structure in microchannels at low Reynold’s numbers is considered. The computational approach is based on the boundary element method accelerated both via an advanced scalable algorithm (FMM), and via utilization of a heterogeneous computing architecture (multicore CPUs and graphics processors). To solve large scale problems flexible GMRES solver is developed. Example computations are conducted for dynamics of many deformable drops of different sizes in microchannels. The results of simulations and accuracy/performance of the method are discussed. The developed approach can be used for solution of a wide range of problems related to emulsion flows in micro- and nanoscales.Copyright

Boundary Element Modeling of Dynamics of a Bubble in Contact with a Solid Surface at Low Reynolds Numbers

In the present study, the dynamics of a bubble attached to the surface and driven by the acoustic field at low Reynolds numbers are considered. The approach is based on the boundary element method (BEM) for Stokes flows, which is especially effective for the numerical solution of problems in the three-dimensional case. However, the dynamics of computing compressible bubbles are difficult to formulate due to the degeneration of the conventional BEM for Stokes equations. In the present approach, an additional relation based on the Lorenz reciprocity principle is used to resolve the problem. To describe the contact line dynamics a semiempirical law of motion is used. Such an approach allows us to bypass the known issue of nonintegrability stresses in the moving triple point. The behavior of a bubble attached to the surface in the cases of a pinned or moving contact line is studied. The developed method can be used for the detailed study of bubble dynamics in contact with a solid wall in order to determine the optimal conditions and parameters of surface cleaning processes.

GPU Acceleration of Bubble-Particle Dynamics Simulation

Clusters containing bubbles and solid particles are used in many fields of industry. For instance, the study of bubble-particle interaction can be useful for surface cleaning in microelectronics and froth flotation in oil distillation.

Boundary Element Simulations of Free and Forced Bubble Oscillations in Potential Flow

The study of shrinking, expanding, and strongly interacting bubbles at high Reynolds numbers is of significant interest for micro- and nanotechnologies. One of such interests is related to self-propulsion of bubbles due to non-linear interaction of bubble shape modes. In the present study bubble dynamics in potential flow is considered. The boundary element method (BEM) which offers a low computational cost and provides an accurate representation of bubble surface is employed for studies. To accelerate computations and increase problem size the fast multipole method (FMM) and graphics processors (GPUs) are used. For mesh stabilization, which appears to be an issue, a new parametric spherical filter based on spherical harmonic expansion is developed and implemented. The dynamics of high order surface modes of bubble at free and forced bubble oscillations is studied.© 2014 ASME

Boundary Element Simulations of Compressible Bubble Dynamics in Stokes Flows

Modeling of dynamics of compressible bubbles in acoustic fields at low Reynolds numbers is of interest for a number of contemporary micro- and nanotechnologies. Despite the boundary element method (BEM) is an appropriate method to simulate deformation of three-dimensional bubbles computation of compressible bubbles dynamics using conventional BEM causes difficulties due to degeneration of the resulting system of equations. In the present approach additional relations based on the Lorentz reciprocity principle are used to resolve the problem. The approach is validated by test simulations of dynamics of single bubbles and bubble clusters including strong bubble-bubble interaction in acoustic fields and shear flows.Copyright