Dynamic reduction of a CH 4 /air chemical mechanism appropriate for investigating vortex–flame interactions

This paper describes two methods, piecewise reusable implementation of solution mapping (PRISM) and dynamic steady‐state approximation (DYSSA), in which chemistry is reduced dynamically to reduce the computational burden in combustion simulations. Each method utilizes the large range in species timescales to reduce the dimensionality to the number of species with slow timescales. The methods are applied within a framework that uses hypercubes to partition multidimensional chemical composition space, where each chemical species concentration, plus temperature, is represented by an axis in space. The dimensionality of the problem is reduced uniquely in each hypercube, but the dimensionality of chemical composition space is not reduced. The dimensionality reduction is dynamic and is different for different hypercubes, thereby escaping the restrictions of global methods in which reductions must be valid for all chemical mixtures. PRISM constructs polynomial equations in each hypercube, replacing the chemical kinetic ordinary differential equation (ODE) system with a set of quadratic polynomials with terms related to the number of species with slow timescales. Earlier versions of PRISM were applied to smaller chemical mechanisms and used all chemical species concentrations as terms. DYSSA is a dynamic treatment of the steady‐state approximation and uses the fast–slow timescale separation to determine the set of steady‐state species in each hypercube. A reduced number of chemical kinetic ODEs are integrated rather than the original full set. PRISM and DYSSA are evaluated for simulations of a pair of counterrotating vortices interacting with a premixed CH 4 /air laminar flame. DYSSA is sufficiently accurate for use in combustion simulations, and when relative errors are less than 1.0%, speedups on the order of 3 are observed. PRISM does not perform as well as DYSSA with respect to accuracy and efficiency. Although the polynomial evaluation that replaces the ODE solver is sufficiently fast, polynomials are not reused sufficiently to enable their construction cost to be recovered. © 2007 Wiley Periodicals, Inc. 39: 204–220, 2007