Local rectangular refinement with application to nonreacting and reacting fluid flow problems

A new solution-adaptive gridding method has been developed for the solution of discretized systems of coupled nonlinear elliptic partial differential equations on rectangular domains. Such a method is required for the numeric al solution of realistic combustion problems, in which physical quantities may vary by orders of magnitude over one-tenth of a millimeter at atmospher ic pressure, or over micrometers at higher pressures. The local rectangular refinement (LRR) method maintains orthogonality at grid-line intersections but lifts the tensor product restriction common to traditional grids, prod ucing unstructured grids. Governing equations are discretized throughout th e domain using newly derived forms, and Newton's method is used to solve th e resulting system. On a simple test case with a known solution, the LRR me thod and its new discretizations are found to be more accurate than griddin g methods representative of those appearing previously in the literature. F or the more realistic problem of nonreacting driven square cavity flow, the LRR solution agrees very well with previously published data. When the LRR method is applied to a practical reacting flow (a rich axisymmetric lamina r Bunsen flame with complex chemistry, multicomponent transport, and an opt ically thin radiation submodel), grid spacing highly influences the inner f lame's position, which stabilizes only with adequate refinement, The vortic ity-velocity formulation of the governing equations is shown to produce val id results when used in conjunction with the LRR gridding technique. Furthe rmore, each LRR grid is used to form a nonuniform equivalent tensor product (ETP) grid and also, in most cases, an equispaced fully refined (FR) grid; these additional grids are supersets of the LRR grids and thus contain ref inement in exactly the same regions. Performance comparisons between the LR R, ETP, and FR grids indicate that the LRR method provides substantial savi ngs in execution time and computer memory requirements, without compromisin g solution accuracy. (C) 1999 Academic Press.