基于非结构网格离散型伴随方法的翼型优化

A discrete adjoint-based approach for airfoil optimization on unstructured meshes

  • 摘要: 发展实现了基于非结构网格离散型伴随方法的气动力优化技术并将其应用于翼型优化。针对以往伴随模型只考虑流场伴随方程而使梯度计算量仍与设计变量数目相关的问题,研究了基于目标函数计算全过程的伴随模型,通过对优化问题整体进行线化、转置运算从而得到完整的伴随模型,实现了梯度计算的计算量与设计变量数目无关的效果。同时针对离散型伴随方法具体推导过程冗长易错的问题,选择性地利用自动微分技术对空间离散过程的各部分进行处理,既避免了盲目使用自动微分导致计算效率低下的问题,又大幅减小了离散型伴随方法具体形式的推导实现难度。翼型反设计问题和约束优化问题计算结果展示了本文方法的有效性。

     

    Abstract: A technique for developing and implementing discrete adjoint methods for airfoil aerodynamic optimization problems on unstructured meshes is presented. Two issues in previous discrete adjoint methods are discussed: the total computational cost is still dependent on the number of design variables in previous discrete adjoint formulation based on flow adjoint equations; and the lengthy and error-prone implementation is usually required to develop adjoint codes. For the first question, the adjoint of the object function is constructed by linearizing each procedure of the entire optimization problem and transposing the total linearization so the computational time required to evaluate the gradient is independent of the number of design variables. For the second question, an automatic differentiation tool is applied selectively to the development of the adjoint code so that a "black-box" application of automatic differentiation tool is avoided and the complexity involved in the development and implementation of discrete adjoint methods is reduced. The inverse design and the constrained optimization results demonstrate the efficiency of the present approach.

     

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