Implementation of gradient based optimizers for reaction mechanism tuning

Detailed reaction mechanisms are often too large for practical Computational Fluid Dynamics (CFD) simulations. Typically, these mechanisms are reduced to an affordable size for its use in CFD simulation. As a consequence of this, the accuracy of the reduced mechanism is compromised. Reaction mechanism tuning is essential to restore the accuracy of the reduced reaction mechanism. This is done by first identifying the most sensitive reactions that affect the quantities of interest (for example, ignition delay, flame-speed etc.) and then running an optimization algorithm to modify those reaction rate parameters to meet the required targets. This paper deals with the implementation of gradient based optimizers for tuning the reaction rate parameters. Based on the zero-dimensional and one-dimensional reactors, a procedure is outlined to obtain the gradients of ignition delay and flame-speed with respect to the reaction rate parameters. A quasi-Newton based LBFGS local optimizer is used which uses the gradient information to arrive at a local minimum within a few objective function evaluations. To obtain the global minimum, two different restart algorithms are used. The first being a simple multi-restart scheme where the local optimizer is called with multiple initial conditions generated using a low discrepancy random sequence generator (Sobol). The second is TikTak, which is a modified version of the first. The performance of the gradient-based optimizer both as a local optimizer as well as in conjunction with restart schemes is demonstrated and also compared with a derivative free global optimizer (DIRECT). Contrary to the common belief, the gradient based optimizers are shown to perform quite well for reaction mechanism tuning, especially in combination with TikTak global optimizer.