Novel Approach to Improve Stability and Convergence of Flowfield Solution Processes: Mode Multigrid

In the field of computational fluid dynamics, stability and convergence problems are often encountered when solving the governing equation. This paper studies the effect of the mode multigrid on the stability and convergence of iterative algorithms. By further analyzing the mechanism for accelerating the convergence of mode multigrid, a new adaptive mode multigrid (AMMG) is proposed, and an adaptive selection criterion is formulated for the parameters of dynamic modal decomposition, which can accurately identify and filter out the unstable modes in the flowfield, thus efficiently obtaining the accurate steady solution. In the cases of laminar flow past circular cylinder and turbulent flow past airfoil, the AMMG significantly improves the stability of the iterative algorithm; in the case of transonic flow past airfoil, the AMMG solves the problem of shock wave shaking during the iteration, and the convergence is significantly improved. In summary, the AMMG method significantly enhances the stability and convergence of the iterative algorithm, and can be used as an effective convergence-preserving computation strategy.