#### Date of Award

2014

#### Degree Type

Dissertation

#### Degree Name

Doctor of Philosophy in Ocean Engineering

#### Department

Ocean Engineering

#### First Advisor

Stephan T. Grilli

#### Abstract

Simulating complex fluid flow have always been one the most challenging problem in Computational Fluid Dynamics (CFD). Most of these difficulties come from the deficiencies of Classical CFD method in computational time and boundary implementations. Recently the Lattice Boltzmann Method (LBM) has been recognized as an alternative to the classical CFD methods for its advantages such as, easy boundary implementation, suitability for parallel simulation and no need for the Poisson pressure solver.

The LBM is based on the Boltzmann equation, which governs the dynamics of molecular probability distribution functions, from a microscopic scale point of view. The primary variable of the Boltzmann equation is the particle distribution function *f*(*x*, *t*, ξ) which describes the probability to find a particle with microscopic velocity ξ at point χ and time *t*. The macroscopic fluid properties (velocities, pressure) are computed as moments of these particle distribution functions.

This dissertation investigates LBM for complex multiphase fluid simulation in three manuscripts. In the first manuscript a novel LBM scheme is developed for simulating multiphase flow simulation with high-density ratio. In previous multiphase flow simulations the maximum fluids density ratio achievable in computations was limited by the occurrence of instabilities for high density ratio values (typically larger than 10-20). Overcoming this limitation is one of the most challenging current issues in the LBM modeling of multiphase flows and the subject of the first manuscripts, as we aim at modeling complex flows at an air-water interface, whose density ratio is about 1,000.

It should be pointed out that although the numerical scheme in manuscript one is able to simulate large density ratio multiphase flow for moderate Reynolds numbers it is not stable for high Reynolds numbers. Eliminating this deficiency of the first manuscript for simulating of multiphase flows with high density ratios and high Reynolds numbers is the subject of second manuscript. In the second manuscript a novel LBM method is introduced which is able to simulate multiphase flow with arbitrary Reynolds and density ratios. The resulting algorithm is applied to several test cases, such as droplet splash, rising bubble and wave braking. The good agreement between numerical results and existing data demonstrate that the newly developed model is a useful tool for simulating complex multiphase flows.

In the third manuscript we study the effects of point-wise particles on turbulent channel flow. Investigating particle-laden turbulent flows is an important fluid mechanics problem as it occurs frequently in nature. This work has been done in collaboration with Professor Tetsu Hara and Yackar Mauzole in Graduate School of Oceanography at the University of Rhode Island to study the sea spray generation effects of turbulent layer above see surface in high wind condition. In this work the Lattice Boltzmann method is coupled to a Lagrangian particle tracking approach for simulating a system of fluid-particle flow.

In all three manuscripts the numerical schemes are developed in nVIDIA CUDA framework, which made it possible to efficiency implemented on General Purpose Graphical Processing Unit (GPGPU) to numerously increase the computational speed of the numerical code.

#### Recommended Citation

Banari, Amir, "Lattice Boltzmann Simulation of Multiphase Flows; Application to Wave Breaking and Sea Spray Generation" (2014). *Open Access Dissertations.* Paper 282.

http://digitalcommons.uri.edu/oa_diss/282

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