A Hybrid Discontinuous Galerkin-Monte Carlo Simulator for Filtered Density Function

A new computational scheme is developed for large eddy simulation (LES) of compressible turbulent reacting flows via the filtered density function (FDF) subgrid scale closure. This is a hybrid scheme, combining the discontinuous Galerkin (DG) Eulerian solver with a Lagrangian Monte Carlo FDF simulator. 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. Simulations are conducted of both incompressible and compressible flows. The consistency and the overall performance of the DG-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. It is also shown that the scheme is capable of accurate simulation of shock dominated flows