| In this dissertation we develop a novel approach to the computational modelling of turbulent flows. Our new method combines large-eddy simulation (LES) with the one-dimensional turbulence (ODT) model of Kerstein [41]. The LES equations result from spatial filtering of the Navier-Stokes equations, the fundamental equations of fluid mechanics. Filtering reduces computational cost by smoothing the solution but generates a new term, the "subgrid stress," which must be modelled (i.e., closed). This term can be interpreted as the stress due to unresolved advective motions across a control volume surface. ODT, adopted here as the subgrid stress model, addresses key limitations of LES, namely, the need to explicitly account for small-scale variation in temperature and species concentrations for chemically reacting flows and the need to resolve the near-wall shear stress in boundary layer flows. Our method has the power to dynamically bridge across orders of magnitude in Reynolds number (a measure of the degree of turbulence) between the three-dimensional, energy-containing scales of motion and the isotropic, dissipative scales where molecular processes dominate. ODT models diffusion along a 1d line using molecular transport coefficients. Turbulent advection along the line is modelled by stochastic mapping events. The mappings rearrange fluid elements in a conservative way and increase the local strain, thereby increasing the likelihood of future events and generating a cascade of length scales characteristic of turbulent flows. The method developed here is validated for decaying isotropic turbulence and extended to multi-processor calculations using a portable set of Fortran kernels called the "LESODT tool kit." To some degree, coupling to LES alleviates the need to empirically tune the ODT rate constant. In this thesis we also develop a simplified ODT model ("ensemble mean closure") where mapping events act upon a velocity field linearized by the local LES strain and do not affect the probability of future events. The linearization allows analytic determination of the rate constant through an equilibrium analysis, and, to leading order, this constant matches the empirically observed values. |
