Accelerated Convergence Method for Flow Field Based on DMD-POD Combined Reduced-Order Optimization Model

Abstract

This work presents a novel acceleration method that achieves more efficient convergence of steady-state flow fields. This method involves conducting dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD) model reduction on the field snapshots. Subsequently, the residual of the reduced-order model is optimized in the POD modal space to obtain a more accurate solution. This optimized solution is then used as the initial field, and the solver continues iterating until the residual converges. Taking full advantage of both DMD and POD, the proposed approach removes the interference of high-frequency oscillatory flow components and concentrates on the main energy components. This effectively overcomes the problems of slow convergence and residual jumps caused by system stiffness, thereby accelerating the convergence process. The results show that for linear equations, the proposed method achieves a significant acceleration, with a convergence speed five times faster than traditional numerical methods. For the nonlinear Burgers equation, the proposed method also reduces the number of convergence steps by nearly 70%. Additionally, the performance of the proposed accelerated convergence method was further validated through the complex flow around a high-dimensional dual ellipsoid.