Investigating stiffness detection metrics for chemical kinetics ODEs

2017-03-07T05:16:36Z (GMT) by Andrew T Alferman Kyle Niemeyer
<div><b>Talk presented at SIAM CSE17</b></div><div><br></div><div><b>Abstract:</b></div>Many simulations of combustion and reactive flows 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 combustion simulations rely on these methods by default. However, if chemical kinetics systems exhibit low-to-moderate stiffness, explicit or stabilized explicit methods can instead be used to reduce the computational expense (while remaining stable and accurate). This study therefore aims to determine a stiffness quantification metric capable of efficiently and robustly determining the appropriate category of integrator required. Literature stiffness quantification methods will be surveyed and investigated as metrics to measure the stiffness of chemical kinetics states, 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 methane autoignition with different initial conditions, and evaluated in terms of effectiveness and computational efficiency.