@article{QIN2025, 
author = {Xueyu QIN and Jian YU and Xin ZHANG and Zhenhua JIANG and Chao YAN},
title = {Novel adaptive IMEX two-step Runge-Kutta temporal discretization methods for unsteady flows},
year = {2025},
journal = {Chinese Journal of Aeronautics},
volume = {38},
number = {8},
keywords = {Implicit-explicit temporal methods, Two-step Runge-Kutta methods, Adaptive algorithm, Unsteady flows, Navier-Stokes equations},
url = {https://www.sciopen.com/article/10.1016/j.cja.2025.103442},
doi = {10.1016/j.cja.2025.103442},
abstract = {Efficient and accurate simulation of unsteady flow presents a significant challenge that needs to be overcome in computational fluid dynamics. Temporal discretization method plays a crucial role in the simulation of unsteady flows. To enhance computational efficiency, we propose the Implicit-Explicit Two-Step Runge-Kutta (IMEX-TSRK) time-stepping discretization methods for unsteady flows, and develop a novel adaptive algorithm that correctly partitions spatial regions to apply implicit or explicit methods. The novel adaptive IMEX-TSRK schemes effectively handle the numerical stiffness of the small grid size and improve computational efficiency. Compared to implicit and explicit Runge-Kutta (RK) schemes, the IMEX-TSRK methods achieve the same order of accuracy with fewer first derivative calculations. Numerical case tests demonstrate that the IMEX-TSRK methods maintain numerical stability while enhancing computational efficiency. Specifically, in high Reynolds number flows, the computational efficiency of the IMEX-TSRK methods surpasses that of explicit RK schemes by more than one order of magnitude, and that of implicit RK schemes several times over.}
}