Development and application of Lattice Boltzmann and accurate volume of fluid numerical techniques on graphics processing units

The research work presented in this dissertation is concerned with development and applications of two computational techniques for high density ratio two-phase flow as encountered in air conditioning and refrigeration equipment. In this research work, we have examined mesoscopic and macroscopic approaches of CFD modeling for multiphase calculations. We have examined two variants of two-phase Lattice Boltzmann methods (LBM) namely the Shan and Chen (SC) and He and Chen (HC) and applied them to study various flows including droplet impingement on solid and liquid surfaces, head-on and oblique droplet collisions, droplet deformation in a square duct, and displacement flow in complex micro-channels. Both SC and HC methods were able to model liquid-liquid flow, whose density ratio is less than 2, but both methods were unstable for gas-liquid flow. To handle large density ratios, we have developed an alternate finite volume based computational technique where continuity, momentum, and interface tracking equations are solved. The volume of fluid (VOF) method is used for accurate representation and tracking of the interface, and a pressure balance method is used for pressure gradient and other discontinuous body forces in the Navier-Stokes equation. The interfacial force is modeled using the sharp surface force (SSF) method, and an additional Poisson equation is derived for the pressure due to surface tension forces. This method is stable for flow involving density and viscosity ratios up to 1000 and 100 respectively. We have applied the computational technique to various fundamental problems to verify its accuracy and robustness. The study of an air bubble rising in a viscous liquid is used to validate the computational technique with experimental results. The effects various dimensionless parameters (Bond number, Morton number, and confinement ratio) were investigated to understand the terminal velocity and shape of a bubble. Subsequently, bubble dynamics in variable viscosity fluid were investigated where the effects of power-law index, Bond number, and confinement ratio have been analyzed on the bubble deformation, rise velocity, and rise path. Finally, the dynamics of a bubble swarm in a square duct is simulated. The modification of turbulence due to the introduction of bubbles is studied. This problem required handling of multiple interfaces, wall-interface interaction, and interface-interface interaction, and tested the robustness of the VOF method. We validated the turbulence implementation by comparing the mean quantities with literature for unladen flow. A sizable number of spherical bubbles are introduced in the unladen flow, and their movement is tracked until a stationary state is reached. We compared flow structures, mean and instantaneous velocities, and various turbulence quantities between unladen and laden flows. We also investigated the mechanism for preferential distribution of bubbles in an upward turbulent bubbly flow. Both LBM procedures and VOF are implemented to run on graphics processing units (GPU) including multiple CPU-GPU platforms. The throughput of a single GPU LBM code is approximately 16 times higher that of a single CPU code. The scaling of a multi-GPU VOF code is nearly linear on the Blue Waters computing facility. The numerical method developed in this study is useful for the study of a variety of two-phase flow, including those with heat transfer and phase change. Such flow will be considered in the future