A mean-error-based time-step control method for detonation simulation

To improve the computational efficiency in implicit-explicit (IMEX) algorithms for stiff detonation problems, the Mean Error Time Control (METC) method is proposed. The core of METC is a novel selected full-field error estimation. This method estimates the full-field error by averaging the errors in regions of significant stiffness. An error controller with integral (I) feedback is then used to determine the neighboring time-step ratios to obtain time-steps within the IMEX stability range. This new strategy ensures a larger time-step while maintaining higher simulation accuracy and making the time-step change more smoothly, providing a reasonable approximation of full-field time error. It is been tested on one-dimensional, two-dimensional oblique, and rotating detonation cases. Compared with the fixed Courant-Friedrichs-Lewy number method, the METC method achieves speedup ratios of 1.48-5.60 for all types of detonation problems related to hydrogen fuels, and the speedup ratio is up to 4.67 for hydrocarbon fuels with greater stiffness. The METC method overcomes the inefficiencies caused by too small a time-step in the Proportional-Integral method in multidimensional reaction flows.