Efficient computations for multiphase flow problems using coupled lattice Boltzmann-level set methods

Abstract

Multiphase flow simulations benefit a variety of applications in science and engineering as for example in the dynamics of bubble swarms in heat exchangers and chemical reactors or in the prediction of the effects of droplet or bubble impacts in the design of turbomachinery systems. Despite all the progress in the modern computational fluid dynamics (CFD), such simulations still present formidable challenges both from numerical and computational cost point of view. Emerging as a powerful numerical technique in recent years, the lattice Boltzmann method (LBM) exhibits unique numerical and computational features in specific problems for its ability to detect small scale transport phenomena, including those of interparticle forces in multiphase and multicomponent flows, as well as its inherent advantage to deliver favourable computational efficiencies on parallel processors. In this thesis two classes of LB methods for multiphase flow simulations are developed which are coupled with the level set (LS) interface capturing technique. Both techniques are demonstrated to provide high resolution realizations of the interface at large density and viscosity differences within relatively low computational demand and regularity restrictions compared to the conventional phase-field LB models. The first model represents a sharp interface one-fluid formulation, where the LB equation is assigned to solve for a single virtual fluid and the interface is captured through convection of an initially signed distance level set function governed by the level set equation (LSE). The second scheme proposes a diffuse pressure evolution description of the LBE, solving for velocity and dynamic pressure only. In contrast to the common kineticbased solutions of the Cahn-Hilliard equations, the density is then solved via a mass conserving LS equation which benefits from a fast monolithic reinitialization. Rigorous comparisons against established numerical solutions of multiphase NS equations for rising bubble problems are carried out in two and three dimensions, which further provide an unprecedented basis to evaluate the effect of different numerical and implementation aspects of the schemes on the overall performance and accuracy. The simulations are eventually applied to other physically interesting multiphase problems, featuring the flexibility and stability of the scheme under high Re numbers and very large deformations. On the computational side, an efficient implementation of the proposed schemes is presented in particular for manycore general purpose graphical processing units (GPGPU). Various segments of the solution algorithm are then evaluated with respect to their corresponding computational workload and efficient implementation outlines are addressed.