In this paper we describe the numerical analysis underlying our efforts to develop an accurate and reliable code for simulating flame propagation using complex physical and chemical models. We discuss our spatial and temporal discretization schemes, which in our current implementations range in order from two to six. In space we use staggered meshes to define discrete divergence and gradient operators, allowing us to approximate complex diffusion operators while maintaining ellipticity. Our temporal discretization is based on the use of preconditioning to produce a highly efficient linearly implicit method with good stability properties. High order for time accurate simulations is obtained through the use of extrapolation or deferred correction procedures. We also discuss our techniques for computing stationary flames. The primary issue here is the automatic generation of initial approximations for the application of Newton's method. We use a novel time-stepping procedure, which allows the dynamic updating of the flame speed and forces the flame front towards a specified location. Numerical experiments are presented, primarily for the stationary flame problem. These illustrate the reliability of our techniques, and the dependence of the results on various code parameters. Hagstrom, Thomas and Radhakrishnan, Krishnan and Zhou, Ruhai Glenn Research Center NASA/CR-1999-209305, NAS 1.26:209305, AIAA Paper 98-3246, ICOMP-99-07, E-11826

The objective of the present program is to study the structure and response of steady and unsteady laminar premixed and nonpremixed flames in reduced and elevated pressure environments through (a) non-intrusive experimentation, (b) computational simulation using detailed flame and kinetic codes, and (c) asymptotic analysis with reduced kinetic mechanisms. During the reporting period progress has been made in the following projects: (1) a theoretical and experimental study of unsteady diffusion flames; (2) a computational and experimental study of methane/air flames at elevated pressures; (3) an asymptotic analysis of the structure of methane/air premixed flames with reduced chemistry; (4) an asymptotic analyses of the extinction of laminar premixed flames with volumetric heat loss and chain mechanisms; and (5) asymptotic analyses of ignition in the supersonic laminar flat-plate boundary layer and mixng layer. A total of five reprints are appended.

The objective of the present program is to study the structure and response of steady and unsteady laminar premixed and nonpremixed flames in reduced and elevated pressure environments through (a) non-intrusive experimentation, (b) computational simulation using detailed flame and kinetic codes, and (c) asymptotic analysis with reduced kinetic mechanisms. During the reporting period progress has been made in the following projects: (1) a theoretical and experimental study of unsteady diffusion flames; (2) a computational and experimental study of methane/air flames at elevated pressures; (3) an asymptotic analysis of the structure of methane/air premixed flames with reduced chemistry; (4) an asymptotic analysis of the extinction of laminar premixed flames with volumetric heat loss and chain mechanisms; and (5) asymptotic analyses of ignition in the supersonic laminar flat-plate boundary layer and mixing layer. A total of five reprints are appended. Flames, High-pressure combustion, Unsteady combustion, Reduced mechanisms, Methane-air flames, Extinction, Supersonic combustion.