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 numerical solution of realistic combustion problems, in which physical quantities may vary by orders of magnitude over one-tenth of a millimeter at atmospheric 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, producing unstructured grids. Governing equations are discretized throughout the domain using newly derived forms, and Newton's method is used to solve the resulting system. On a simple test case with a known solution, the LRR method and its new discretizations are found to be more accurate than gridding methods representative of those appearing previously in the literature. For 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 laminar Bunsen flame with complex chemistry, multicomponent transport, and an optically thin radiation submodel), grid spacing highly influences the inner flame's position, which stabilizes only with adequate refinement, The vorticity-velocity formulation of the governing equations is shown to produce valid results when used in conjunction with the LRR gridding technique. Furthermore, 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 refinement in exactly the same regions. Performance comparisons between the LRR, ETP, and FR grids indicate that the LRR method provides substantial savings in execution time and computer memory requirements, without compromising solution accuracy. (C) 1999 Academic Press.