Local rectangular refinement with application to axisymmetric laminar flames

Within realistic combustion devices, physical quantities may change by an order of magnitude over an extremely thin flamefront, while remaining nearly unchanged throughout large areas nearby. Such behaviour dictates the use of adaptive numerical methods. The recently developed local rectangular refinement (LRR) solution-adaptive gridding method produces robust unstructured rectangular grids, utilizes novel multiple-scale finite-difference discretizations, and incorporates a damped modified Newton's method for simultaneously solving systems of governing elliptic PDEs. Here, the LRR method is applied to two axisymmetric laminar flames: a premixed Bunsen flame with one-step chemistry and a diffusion flame employing various complex chemical mechanisms. The Bunsen flame's position is highly dependent upon grid spacing, especially on coarse grids; it stabilizes only with adequate refinement. The diffusion flame results show excellent agreement with experimental data for flame structure, temperature and major species. For both dames, the LRR results on intermediate grids are comparable to those obtained on equivalently refined conventional grids. Solution accuracy on the final LRR grids could not be achieved using conventional grids because the latter exceeded the available computer memory. In general, the LRR method required about half the grid points, half the memory and half the computation time of the solution process on conventional grids.