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首页> 外文期刊>Chinese Journal of Aeronautics >A Preconditioned Multigrid Method for Efficient Simulation of Three-dimensional Compressible and Incompressible Flows
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A Preconditioned Multigrid Method for Efficient Simulation of Three-dimensional Compressible and Incompressible Flows

机译：一种用于高效模拟三维可压缩和不可压缩流动的预处理多网格方法

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摘要

To develop an efficient and robust aerodynamic analysis method for numerical optimization designs of wing and complex configuration, a combination of matrix preconditioning and multigrid method is presented and investigated. The time derivatives of three-dimensional Navier-Stokes equations are preconditioned by Choi-Merkle preconditioning matrix that is originally designed for two-dimensional low Mach number viscous flows. An extension to three-dimensional viscous flow is implemented, and a method improving the convergence for transonic flow is proposed. The space discretizaition is performed by employing a finite-volume cell-centered scheme and using a central difference. The time marching is based on an explicit Runge-Kutta scheme proposed by Jameson. An efficient FAS multigrid method is used to accelerate the convergence to steady-state solutions. Viscous flows over ONERA M6 wing and M100 wing are numerically simulated with Mach numbers ranging from 0.010 to 0.839. The inviscid flow over the DLR-F4 wing-body configuration is also calculated to preliminarily examine the performance of the presented method for complex configuration. The computed results are compared with the experimental data and good agreement is achieved. It is shown that the presented method is efficient and robust for both compressible and incompressible flows and is very attractive for aerodynamic optimization designs of wing and complex configuration.
机译：为了建立一种高效、鲁棒的机翼数值优化和复杂构型气动分析方法，提出并研究了矩阵预处理和多网格方法的结合。三维纳维-斯托克斯方程的时间导数由Choi-Merkle预处理矩阵进行预处理，该矩阵最初是为二维低马赫数粘性流动而设计的。实现了对三维粘性流动的扩展，并提出了一种提高跨音速流动收敛性的方法。空间离散化是通过采用有限体积的单元中心方案并使用中心差分来执行的。时间行进是基于詹姆逊提出的明确的 Runge-Kutta 方案。采用一种高效的FAS多网格方法加速了向稳态解的收敛。对ONERA M6机翼和M100机翼上的粘性流动进行了数值模拟，马赫数范围为0.010至0.839。还计算了DLR-F4翼体构型上的无粘性流动，以初步检验所提方法在复杂构型下的性能。将计算结果与实验数据进行比较，结果较好。结果表明，所提方法对可压缩和不可压缩流动均具有高效和鲁棒性，对机翼和复杂构型的气动优化设计具有很强的吸引力。

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