Resolution estimates for simple one-dimensional flames

The accurate resolution of flame structure is critically important to the direct numerical simulation of reacting flows. While grid-resolution estimates are readily available for cold flows, premixed flames appear to have received relatively little attention. In this paper, a premixed flame characterised by single-step chemistry at moderate-to-high Zel'dovitch numbers (β) is analysed, and its structure is used to provide estimates for sufficient grid resolution. It is found that the critical region of the flame exhibits a weak inverse Zel'dovitch number dependence, and that heuristic methods of resolution estimation based on flame thickness grow relatively less meaningful as β → ∞. Resolution estimates for second- and fourth-order finite-difference schemes are provided.