AERODYNAMIC SENSITIVITY ANALYSIS FOR NAVIER-STOKES EQUATIONS
AERODYNAMIC SENSITIVITY ANALYSIS FOR NAVIER-STOKES EQUATIONS
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纳维-斯托克斯方程的空气动力学敏感性分析
DOI：
10.2514/6.1999-402
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发表时间：
1999
影响因子：
0.6
通讯作者：
Ki D. Lee
中科院分区：
文献类型：
--
作者：
H. Kim;Chongam Kim;O. Rho;Ki D. Lee
从二维可压缩Navier-Stokes方程出发，分别采用直接微分法和伴随法，通过手微分法编制了气动灵敏度分析程序。与以往的其他研究不同，Baldwin-Lomax代数湍流模型也是由手微分，以获得设计灵敏度相对于感兴趣的设计变量在湍流流动。离散的直接灵敏度方程和伴随方程的有效解决了相同的时间积分方案中采用的流动求解程序。通过允许大的带状通量雅可比矩阵的未组装，伴随灵敏度代码所需的存储器被大大减少，在计算时间的成本。直接灵敏度程序计算结果与用有限差分法求得的灵敏度导数结果完全一致。伴随程序的湍流情况下的结果显示，由于代数湍流模型在实现伴随公式的限制，从精确的结果略有偏差。然而，目前的伴随灵敏度程序产生更准确的灵敏度导数比伴随程序的湍流涡动粘度保持不变，这是一个通常的假设，为以前的研究。
Aerodynamic sensitivity analysis codes are developed via the hand-differentiation using a direct differentiation method and an adjoint method respectively from discrete two-dimensional compressible Navier-Stokes equations. Unlike previous other researches, Baldwin-Lomax algebraic turbulence model is also differentiated by hand to obtain design sensitivities with respect to design variables of interest in turbulent flows. Discrete direct sensitivity equations and adjoint equations are efficiently solved by the same time integration scheme adopted in the flow solver routine. The required memory for the adjoint sensitivity code is greatly reduced at the cost of the computational time by allowing the large banded flux jacobian matrix unassembled. Direct sensitivity code results are found to be exactly coincident with sensitivity derivatives obtained by the finite difference. Adjoint code results of a turbulent flow case show slight deviations from the exact results due to the limitation of the algebraic turbulence model in implementing the adjoint formulation. However, current adjoint sensitivity code yields much more accurate sensitivity derivatives than the adjoint code with the turbulence eddy viscosity being kept constant, which is a usual assumption for the prior researches.