Time-scale splitting-based mechanism reduction

Chemical reaction systems, including those in combustion, often exhibit a large range of time-scales which can lead to stiffness in the resulting rate equations. This feature can however be exploited in the context of model reduction by recognising that certain fast species can relax to a quasi-equilibrium state or, in geometrical terms, that the evolution of the system of equations in composition space relaxes to lower and lower dimensional attractors. Time-scale separation therefore forms a basis for model reduction. This chapter introduces model reduction techniques based on time-scale splitting which may differ in their approach, but which all utilise the fact that chemical kinetic systems evolve with time-scales that often differ by orders of magnitude. The chapter will first discuss the mathematical basis on which time-scale separation is defined. It will then discuss approaches for model reduction based on algebraic approximations such as the quasi-steady state approximation or QSSA, trajectory-based approaches such as computational singular perturbation methods, geometrical approaches based on the presence of intrinsic low dimensional manifolds in composition space and methods based on thermodynamic principles such as the rate-controlled constrained-equilibrium method. Methods will be introduced for homogeneous reaction systems. The extension to reaction diffusion systems will then be discussed.