A High-Order Finite-Volume Scheme for Large-Eddy Simulation of Turbulent Premixed Flames

Abstract

A novel, parallel, high-order, central essentially non-oscillatory (CENO), cell-centered, finite-volume scheme is developed and applied to large-eddy simulation (LES) of turbulent premixed flames. The high-order CENO finite-volume scheme is applied to the solution of the Favre-filtered Navier-Stokes equations governing turbulent flows of a fully-compressible reactive mixture on three-dimensional, multi-block, body-fitted, computational mesh consisting of hexahedral volume elements. Unlike standard ENO schemes, which require solution reconstruction on multiple stencils, the CENO method uses a hybrid reconstruction approach based on a fixed central stencil, thereby avoiding the complexities of other ENO schemes while providing high-order accuracy at relatively lower computational cost. The CENO discretization of the inviscid fluxes combines an unlimited high-order k-exact leastsquares reconstruction technique based on the optimal central stencil with a monotonicitypreserving, limited, linear, reconstruction algorithm. Switching in the hybrid procedure is determined by a smoothness indicator such that the unlimited high-order reconstruction is retained for smooth solution content that is fully resolved and reverts to the limited lower-order scheme, enforcing solution monotonicity, for regions with abrupt variations (i.e., discontinuities and under-resolved regions). The high-order viscous fluxes are computed to the same order of accuracy as the hyperbolic fluxes based on a k-order accurate cell interface gradient derived from the unlimited, cell-centered, reconstruction. The proposed cell-centered finite-volume scheme is formulated for three-dimensional multi-block mesh consisting of generic hexahedral cells and applied to LES of premixed flames.For the reactive cases flows of interest, a flamelet-based subfilter-scale (SFS) model is used to describe the unresolved influences of interaction between the turbulence and combustion. This SFS combustion model is based on a presumed conditional moment (PCM) approach in conjunction with flame prolongation of intrinsic low-dimensional manifold (FPI) tabulated chemistry. Numerical results are discussed for a freely propagating flame in an isotropic turbulence field and for a laboratory-scale lean premixed methane-air Bunsentype flame. The performance of the proposed high-order scheme for turbulent reactive flows is discussed.