A novel computational approach, Two Level Simulation (TLS), was developed based on the explicit reconstruction of the small-scale velocity by solving the small-scale governing equations on the domain with reduced dimension representing a collection of one-dimensional lines embedded in the three-dimensional flow domain. A coupled system of equations, that is not based on an eddy-viscosity hypothesis, was derived based on the decomposition of flow variables into the large-scale and the small-scale components without introducing the concept of filtering. Simplified treatment of the small-scale equations was proposed based on modeling of the small-scale advective derivatives and the small-scale dissipative terms in the directions orthogonal to the lines. TLS approach was tested to simulate benchmark cases of turbulent flows, including forced isotropic turbulence, mixing layers and well-developed channel flow, and demonstrated good capabilities to capture turbulent flow features using relatively coarse grids.

<p>This thesis is concerned with particle subgrid scale (SGS) modeling in large-eddy simulation (LES) of particle-laden turbulence. Although most particle-laden LES studies have neglected the effect of the subgrid scales on the particles, several particle SGS models have been proposed in the literature. In this research, the approximate deconvolution method (ADM), and the stochastic models of Fukagata et al. (2004), Shotorban and Mashayek (2006) and Berrouk et al. (2007) are analyzed. The particle SGS models are assessed by conducting both a priori and a posteriori tests of a periodic box of decaying, homogeneous and isotropic turbulence with an initial Reynolds number of Re=74. The model results are compared with particle statistics from a direct numerical simulation (DNS). Particles with a large range of Stokes numbers are tested using various filter sizes and stochastic model constant values. Simulations with and without gravity are performed to evaluate the ability of the models to account for the crossing trajectory and continuity effects. The results show that ADM improves results but is only capable of recovering a portion of the SGS turbulent kinetic energy. Conversely, the stochastic models are able to recover sufficient energy, but show a large range of results dependent on Stokes number and filter size. The stochastic models generally perform best at small Stokes numbers. Due to the random component, the stochastic models are unable to predict preferential concentration.</p> / Master of Applied Science (MASc)