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Trisjono, P.,Kang, S.,Pitsch, H. Academic Press 2016 Journal of computational physics Vol.327 No.-
The main objective of this study is to present an accurate and consistent numerical framework for turbulent reacting flows based on a high-order finite difference (HOFD) scheme. It was shown previously by Desjardins et al. (2008) [4] that a centered finite difference scheme discretely conserving the kinetic energy and an upwind-biased scheme for the scalar transport can be combined into a useful scheme for turbulent reacting flows. With a high-order spatial accuracy, however, an inconsistency among discretization schemes for different conservation laws is identified, which can disturb a scalar field spuriously under non-uniform density distribution. Various theoretical and numerical analyses are performed on the sources of the unphysical error. From this, the derivative of the mass-conserving velocity and the local Peclet number are identified as the primary factors affecting the error. As a solution, an HOFD stencil for the mass conservation is reformulated into a flux-based form that can be used consistently with an upwind-biased scheme for the scalar transport. The effectiveness of the proposed formulation is verified using two-dimensional laminar flows such as a scalar transport problem and a laminar premixed flame, where unphysical oscillations in the scalar fields are removed. The applicability of the proposed scheme is demonstrated in an LES of a turbulent stratified premixed flame.