Application of the Slow Invariant Manifold Correction for Diffusion

Slow invariant manifolds (SIM) are calculated for spatially inhomogeneous closed reactive systems to obtain a model reduction. A robust method of constructing a onedimensional SIM by calculating equilibria and then integrating along heteroclinic orbits is extended to two new cases: i) adiabatic systems, and ii) spatially inhomogeneous systems with simple diffusion. The adiabatic condition can be modeled as a new algebraic constraint in the limit of unity Lewis number. Diffusion effects on the SIM are examined for systems with small characteristic lengths. A diffusion correction is obtained by using a Galerkin method to project the infinite dimensional dynamical system onto a low dimensional approximate inertial manifold. This projection rigorously accounts for the coupling of reaction and diffusion processes, and an analytic length and time scale coupling is shown. An example is demonstrated on a system of NO production which highlights the correlation between an established isothermal spatially homogeneous technique and the new techniques.