Investigating stiffness detection metrics for chemical kinetics

摘要

Simulations of combustion and reactive flows often exhibit numerical stiffness in the equations governing chemical kinetics. Explicit solvers for these equations offer low computational expense, but typically cannot handle stiff systems of differential equations. In contrast, implicit methods demand greater expense but offer unconditional stability-as a result, most non-DNS reactive flow solvers rely on these methods by default. However, explicit or stabilized explicit methods can instead be used to reduce the computational expense while remaining stable and accurate if the chemical kinetics systems exhibit low-to-moderate stiffness. This study aims to investigate stiffness quantification metrics, with the goal of identifying one capable of efficiently and robustly determining the appropriate category of integrator required. Literature on stiffness quantification will be surveyed and methods of measuring the stiffness of chemical kinetics states will be investigated, including methods based on eigendecomposition or the spectral radius of the Jacobian matrix, error estimations, conditioning parameters, and computational cost estimations. These methods will be applied during the solution of hydrogen and carbon monoxide autoignition with different initial conditions based on partially stirred reactor simulation sampling, and evaluated in terms of effectiveness and computational efficiency.