Accelerating CFD simulation: A new adaptive IMEX temporal discretization method

Computational Fluid Dynamics (CFD) is a pivotal tool in modern engineering and scientific research. It utilizes advanced numerical algorithms to simulate complex fluid behavior and related physical processes, with applications spanning aerospace design, energy systems, biomedical engineering, and environmental studies. Yet increasing simulation scale, especially for modeling unsteady flows, leads to significantly higher computational costs and extended processing times. Consequently, achieving efficient and accurate simulations remains a central challenge in CFD.

Recently, a team of computational simulation by Chao Yan from Beihang University, China, have demonstrated that temporal discretization methods directly impact computational speed, and subsequently developed a novel acceleration methodology for CFD simulations. They proposed implicit-explicit (IMEX) two-step Runge-Kutta time-stepping discretization methods for unsteady flows, and investigated a novel adaptive algorithm that correctly partitions spatial regions to apply implicit or explicit methods. The novel adaptive IMEX schemes effectively handle the numerical stiffness of the small grid size and improve computational efficiency.

The team published their study in Chinese Journal of Aeronautics on February 27, 2025.

The IMEX schemes apply the implicit temporal method to only a small portion of the domain and use explicit calculations elsewhere, based on a convenient splitting algorithm. This differs from classical temporal methods, which require either implicit or explicit calculations throughout the entire simulation. IMEX methods effectively combine the advantages of implicit and explicit methods, such as allowing unrestricted time steps and reducing memory requirements for iterative solutions. These advantages enable the IMEX method to demonstrate outstanding performance in computing unsteady flows, especially for a large number of meshes.

In the numerical example, tests are conducted on 30 million grids. The computational efficiency of the IMEX temporal method exhibits a linear growth trend as the time step increases. When the proportion of implicit method calculations is approximately 10%, the IMEX method achieves its maximum computational speedup, improving efficiency by one to two orders of magnitude. The IMEX method can accurately capture complex flow structures, and the numerical results show good agreement with experimental data.

The IMEX method requires implicit calculations for only a very small portion of the grid, while using an explicit method for the majority of areas. This makes it highly suitable for computations involving extremely large-scale meshes, effectively reducing memory requirements of the computer. The IMEX method can achieve efficient parallel computing on supercomputer. In the future, coupling IMEX methods with GPU architectures will achieve greater computational speedups in extreme-scale simulations. This facilitates the acceleration of large-scale, industrial-grade, full-process unsteady numerical simulations.

Other contributors include Xueyu Qin, Jian Yu, Xin Zhang, Zhenhua Jiang from the School of Aeronautic Science and Engineering at Beihang University in Beijing, China.

Original Source

Xueyu QIN, Jian YU, Xin ZHANG, Zhenhua JIANG, Chao YAN. Novel adaptive IMEX two-step Runge-Kutta temporal discretization methods for unsteady flows [J]. Chinese Journal of Aeronautics, 2025, https://doi.org/10.1016/j.cja.2025.103442.

About Chinese Journal of Aeronautics 

Chinese Journal of Aeronautics (CJA) is an open access, peer-reviewed international journal covering all aspects of aerospace engineering, monthly published by Elsevier. The Journal reports the scientific and technological achievements and frontiers in aeronautic engineering and astronautic engineering, in both theory and practice. CJA is indexed in SCI (IF = 5.3, top 4/52, Q1), EI, IAA, AJ, CSA, Scopus.