Intelligent Time-Scale Operator-Splitting Integration for Chemical Reaction Systems

The wide range of time scales in chemical reaction systems has become an important problem in reactive flow simulations. This work proposes an intelligent time-scale operator-splitting (OS) chemistry integration method, which is effective in reduction of numerical stiffness and model complexity. Different from most existing publications, a pretrained backpropagation neural network is used to identify the slow and fast reactions and detect the sources of model stiffness on the fly, which replaces the expensive eigendecomposition of Jacobian matrix. With the fast–slow decomposition, the chemical source term can be represented as the sum of a stiff part and a nonstiff part. A stable time-scale OS integration is performed to solve the stiff chemical ordinary differential equations, which balances the computational cost with accuracy. In the simulation, a favorable comparison of the proposed integration method with the existing ODE solvers, such as implicit Euler, explicit Euler, and Runge–Kutta, is included to show its effectiveness and merits.

I. Introduction

Accurate reactive flow simulations require first-principles chemical kinetic models composed of hundreds of species and thousands of elementary reactions [1], [2]. These kinetic models, always expressed by a set of ordinary differential equations (ODEs), exhibit significant stiffness as a result of a widespread of characteristic time scales associated with reactivity of radical and molecular species [3]–[6]. Due to the large size and chemical stiffness, solving such kinetic models is computationally expensive in terms of CPU time [7]. This poses challenges for the simulation of detailed kinetic models in multidimensional reactive flow simulations, where the ODEs are coupled with partial differential equations (PDEs). In this situation, ODEs are solved on the fly for thousands or millions of times [8], [9].