### 基于降阶模型和梯度优化的流场加速收敛方法

1. 西北工业大学 航空学院，西安 　710072
• 收稿日期:2022-03-01 修回日期:2022-04-24 接受日期:2022-07-14 出版日期:2023-03-25 发布日期:2022-07-21
• 通讯作者: 张伟伟 E-mail:aeroelastic@nwpu.edu.cn
• 基金资助:
国家自然科学基金(92152301)

### Accelerated convergence method for fluid dynamics solvers based on reduced⁃order model and gradient optimization

Wenbo CAO, Yilang LIU, Weiwei ZHANG()

1. School of Aeronautics，Northwestern Polytechnical University，Xi’an 　710072，China
• Received:2022-03-01 Revised:2022-04-24 Accepted:2022-07-14 Online:2023-03-25 Published:2022-07-21
• Contact: Weiwei ZHANG E-mail:aeroelastic@nwpu.edu.cn
• Supported by:
National Natural Science Foundation of China(92152301)

CFD是解决流体相关复杂工程问题的重要手段，随着流体力学研究和工程应用问题的日益复杂，更高效、精确的CFD算法研究至关重要。提出了一种基于降阶模型（ROM）和梯度优化用于加速稳态流场的收敛方法。该方法首先收集CFD迭代求解过程中的流场快照构造基于正交分解（POD）的降阶模型，然后使用梯度优化方法求解降阶模型得到残差更低的流场，最后以该流场为初值继续进行CFD迭代求解从而加速CFD的收敛过程。将该方法用于基于有限体积法的CFD求解器中，针对无黏、湍流算例验证了所提加速收敛方法的有效性。结果表明，加速收敛方法相比于初始CFD方法迭代步数能显著减少2~3倍，是一种高效且鲁棒的加速收敛方法，且在复杂工程问题中具有广泛的应用前景。

Abstract:

Computational Fluid Dynamics（CFD）is an important method to solve fluid-related complex engineering problems. The increasing complexity of fluid mechanics research and engineering applications makes it imperative to explore a more efficient and accurate CFD algorithm. A method based on reduced-order model and gradient optimization is proposed to accelerate the convergence process of fluid dynamics solvers. In this method，the reduced-order model is constructed by the snapshots collected from the iterative process of CFD solvers，and the gradient optimization method is then used to minimize the residual of the reduced-order model. Finally，the flow field with lower residual is selected as the initial condition of the CFD solver to accelerate the convergence process of CFD. The method is applied to the CFD solver based on the finite volume method，and the effectiveness of the proposed method is studied for inviscid and turbulence fluids. The results show that the accelerated convergence method can significantly reduce the number of iterative steps by 2⁃3 times compared with the initial CFD method，exhibiting efficiency，robustness，and a wide application prospect in complex engineering problems.