A Hybrid Filtered Density Function Spectral-Element Large Eddy Simulator

This dissertation is focused on the development of a hybrid scheme, combining the spectral-element method (SEM) solver with a Lagrangian Monte Carlo (MC) filtered density function (FDF) simulator for large eddy simulation (LES) of turbulent flows. The methodology is shown to be suitable for LES, as a larger portion of the resolved energy is captured as the order of spectral approximation increases. The consistency and the overall performance of the SEM-MC solver, and the realizability of the simulated results are demonstrated via LES of a temporally developing mixing layer under both non-reacting and reacting conditions. The effects of grid resolution and polynomial order ($h-p$ refinement), and ensemble average size ($\Delta_E$) are studied. The computational scheme is fully parallelized via the message passing interface (MPI) methodology