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

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.

accepted in J. Comp. Phys

References in corpus (5)

• Quasi Equilibrium Grid Algorithm: geometric construction for model reduction
• Adaptive simplification of complex multiscale systems
• Minimal Curvature Trajectories: Riemannian Geometry Concepts for Model Reduction in Chemical Kinetics
• A variational principle for computing slow invariant manifolds in dissipative dynamical systems
• Fast computation of multi-scale combustion systems

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