Method of invariant manifold for chemical kinetics

TL;DR

This paper reviews the method of invariant manifolds (MIM) for reducing chemical kinetics equations, introduces a thermodynamically consistent version, and discusses grid-based implementations and extensions to open systems.

Contribution

It presents a comprehensive review and new developments of MIM, including thermodynamic consistency, grid-based methods, and extensions to open systems for chemical kinetics reduction.

Findings

Effective reduction of chemical kinetics models

Development of thermodynamically consistent MIM

Introduction of grid-based MIM implementation

Abstract

In this paper, we review the construction of low-dimensional manifolds of reduced description for equations of chemical kinetics from the standpoint of the method of invariant manifold (MIM). MIM is based on a formulation of the condition of invariance as an equation, and its solution by Newton iterations. A review of existing alternative methods is extended by a thermodynamically consistent version of the method of intrinsic low-dimensional manifolds. A grid-based version of MIM is developed, and model extensions of low-dimensional dynamics are described. Generalizations to open systems are suggested. The set of methods covered makes it possible to effectively reduce description in chemical kinetics.