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## Description

The Filtered Density Function (FDF) methodology is combined with a high-order Finite Difference (FD) Weighted Essentially Non-Oscillatory (WENO-Z) flow solver to develop a hybrid solver capable of performing Large Eddy Simulation (LES) for chemically reactive flows. This initial hybrid solver constitutes the introductory steps towards the development of a robust FDF/WENO-Z hybrid solver for the simulation of high-speed, chemically reacting compressible flows. A variable density formulation of the FDF methodology, known as the Scalar Filtered Mass Density Function (S-FMDF) is implemented. This S-FMDF model determines a representation of the filtered density function through a Monte-Carlo approach. The model requires the stochastic tracing of particles that carry the statistical information about the species mass compositions, which are then used to determine the source resulting from the chemical reactions. Solving the modeled S-FMDF transport equation via the hybrid MC/FD scheme yields the chemical source term in closed form. To for high-speed flow with shocks, we approximate the governing systems with a WENO-Z that captures shocks and turbulence with high-fidelity. A WENO-Z flow solver is paired with higher-order ENO interpolations and distribution functions to ensure an accurate tracing of the Monte-Carlo particles that are carried by the flows velocity field and to smoothly distribute the particle grid onto the WENO grid, respectively. In this manner, the WENO-Z based S-FDMF approach preserves the high-fidelity of the WENO-Z scheme The solver is validated against an existing S-FMDF MC/MacCormack FD hybrid solve. Simulation of the Sandia National Laboratories Flame D shows good comparison between the two codes. The WENO-Z based solver produces a smoother solution than the MacCormack based solver, which can be attributed to the inherent dissipation associated with WENO schemes. This suggests that the WENO-Z based solver may be used to perform Implicit Large Eddy Simulation (ILES) by leveraging the inherent dissipation affiliated with WENO schemes to implicitly model the viscous forces in a flow field. ILES is investigated through the simulation of the Sandia National Laboratories’ Flame D by reducing the order of an inviscid WENO-Z solver. The resulting solution compares well with the solution generated by existing viscous MacCormack solver.