A new multi-time-step method for implicit-explicit time integration of incompressible Navier-Stokes equations

초록

Implicit-explicit (IMEX) time integration schemes have emerged as a robust numerical method for simulating problems in computation fluid dynamics. In particular, IMEX schemes in conjunction with the scalar auxiliary variable (SAV) approach are able to achieve unconditional energy stability. However, existing IMEX-SAV schemes are computationally intensive for problems with multiple temporal scales because they are constrained to use the smallest time step necessary to resolve the finest time scale in the entire fluid domain. In this paper, we develop a novel multi-time-step (MTS) method that enables the use of different time steps in different fluid subdomains while maintaining accuracy and unconditional stability. Subdomains with high temporal gradients are integrated with a small step to maintain accuracy whereas other subdomains are integrated with relatively larger time steps to achieve computational efficiency. Dual-Schur domain decomposition (DD) is used to divide the spatial problem domain into several subdomains and continuity of velocity and pressure is simultaneously enforced between the subdomains using Lagrange multipliers. Furthermore, a SAV approach is used to ensure unconditional stability of the method. We show that the method leads to a system of linear algebraic equations thereby eliminating the need for non-linear iterations and reducing the computational cost further. Finally, we demonstrate the performance of the proposed MTS-IMEX-SAV method and highlight the computational gains it achieves compared to conventional IMEX-SAV schemes by solving several benchmark problems. © 2026 Elsevier Inc.

키워드