Efficient computations for multiphase flow problems using coupled lattice Boltzmann-level set methods
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Date
2016-01
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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.
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Keywords
Two-phase flows, Rising bubble benchmarks, Lattice Boltzmann method, Level set method, Numerical simulation, GPGPU implementation