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This paper examines the effect of modelling choices on the numerical simulation of premixed methane/air combustion in narrow channels. Knowledge on standard and well-accepted numerical methods in literature are collected in a cohesive document. The less well-established modelling choices have been thoroughly evaluated and discussed. A systematic method of computing the grid convergence index (GCI) has been presented for refining the computational grid. Two types of inflow boundary conditions have been tested and compared in terms of their wave-damping characteristics. The effect of different reaction schemes on simulation results have been examined and an appropriate mechanism (DRM-19) has been selected. Various types of ignition strategies to initiate the flame have been tested and compared. The transient ignition process which has not been discussed extensively in existing literature has been quantitatively described in this paper. [ABSTRACT FROM AUTHOR]

The goal of this paper is to design a stabilizing feedback boundary control for a reaction–diffusion partial differential equation (PDE), where the boundary control is subject to a constant delay while the equation may be unstable without any control. For this system, which is equivalent to a parabolic equation coupled with a transport equation, a prediction-based control is explicitly computed by splitting the infinite-dimensional system into two parts: a finite-dimensional unstable part and a stable infinite-dimensional part. A finite-dimensional delayed controller is computed for the unstable part, and it is shown that this controller stabilizes the whole PDE. The proof is based on an explicit expression of the classical Artstein transformation combined with an adequately designed Lyapunov function. A numerical simulation illustrates the constructive feedback design method. [ABSTRACT FROM AUTHOR]