基于三维非结构网格的连续伴随优化方法

Continuous Adjoint Approach to Aerodynamic Optimization on 3D Unstructured Grids

基于非结构网格,采用Euler方程、连续伴随方法以及自由形面变形技术(Free-form deformation,FFD)结合序列二次规划(Sequential quadratic programming,SQP)优化算法,开发出了三维飞行器的气动外形优化代码。应用Fortran 90语言,动态存储数组和指针,节省了内存。采用Roe形式的二阶迎风格式和LU-SGS隐式时间离散格式求解连续伴随方程,同时采用一种新的参数化坐标求解方法,使得FFD技术更加鲁棒。和有限差分方法求得的梯度进行比较,验证了连续伴随方法所求梯度的正确性,实现了ONERA M6机翼的减阻优化,证明本文开发的优化代码能够实现三维气动外形的减阻优化。

Based on unstructured grids, codes for 3D aerodynamic shape optimization are developed using Euler equations＇ solution, continuous adjoint method, free-form deformation （FFD） strategy, and se- quential quadratic programming （SQP） optimization method. Fortran 90 is used for the dynamic storage of arrays and pointers and for saving memory. Second-order Roe-type upwind scheme and LU-SGS scheme are used to solve the continuous adjoint equations, and a new approach to computing parametric coordinates is adopted so that FFD can be robuster. The gradients of the adjoint method are compared with those of the finite difference. The designed system is successfully applied to ONERA M6 wing transonic shape optimization with the purpose of reducing drag, and the result shows that the system is reliable and efficient for reducing drag design.