ID#: 124
Abstract Title: Reactive Flow Calculations with Intrinsic Low Dimensional Manifold Corrections for Convection and Diffusion
Session Title: Chemistry in Flames I
Session Date: 7/31/01
Session Start Time: 11:20 AM
Contributing Author: Powers, J.M.
Organization: University of Notre Dame
Country: USA
Authors: Sandeep Singh, Samuel Paolucci, Joseph M. Powers
Short Abstract: A method is described which rationally corrects the method of intrinsic low dimensional manifolds (ILDM) to account for the effects of small convection and diffusion. The ILDM method is well suited for spatially homogeneous problems and provides a systematic way to overcome the severe stiffness which is associated with full models of detailed kinetics and thus significantly improves computational efficiency. Significant errors can arise however when the ILDM method is applied to systems which have convection and diffusion. Motivated by techniques from center manifold theory, and using the ILDM as a reference manifold, we project our entire system of equations onto a new basis, which is segregated into fast and slow sets of equations. The fast scale equations are equilibrated, requiring the solution of an elliptic equation in space. The slow equations are allowed to temporally evolve. Improvements in predictions relative to those of the traditional IDLM method are shown for a simple model problem.