Approximation of slow and fast dynamics in multiscale dynamical systems by the linearized Relaxation Redistribution Method

Authors:
Eliodoro Chiavazzo
Affiliations:
Department of Energetics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
Venue:
Journal of Computational Physics
Year:
2012

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Abstract

In this paper, we introduce a fictitious dynamics for describing the only fast relaxation of a stiff ordinary differential equation (ODE) system towards a stable low-dimensional invariant manifold in the phase-space (slow invariant manifold - SIM). As a result, the demanding problem of constructing SIM of any dimensions is recast into the remarkably simpler task of solving a properly devised ODE system by stiff numerical schemes available in the literature. In the same spirit, a set of equations is elaborated for local construction of the fast subspace, and possible initialization procedures for the above equations are discussed. The implementation to a detailed mechanism for combustion of hydrogen and air has been carried out, while a model with the exact Chapman-Enskog solution of the invariance equation is utilized as a benchmark.