中文摘要：

进行了基于黏性伴随方法和Navier-Stokes方程的跨声速机翼气动优化设计研究。分别推导了适用于三维跨声速机翼气动反设计和减阻设计的黏性伴随方程、边界条件和梯度求解表达式,并研究了伴随方程的数值求解方法。通过将网格生成、流场计算、黏性伴随方程数值求解、梯度求解和拟牛顿优化算法等几方面的有效结合,发展了一种跨声速机翼气动优化设计方法。为了提高计算效率,将多重网格方法应用到方程的数值求解中来加速收敛。跨声速机翼反设计和减阻设计算例验证了本文所发展的方法的正确性。采用本文的方法进行优化设计,一般通过20～30次迭代就能得到满意的结果。

英文摘要：

Aerodynamic shape optimization design of transonic wing is performed based on viscous adjoint method using compressible Reynolds-Averaged Navier-Stokes equations. The viscous adjoint equations, boundary conditions and gradient formulas for inverse design and drag minimization design of viscous flow are derived. A numerical method is developed for solving adjoint equations. The procedure of optimization has been established by an effective combination of grid generation, flow and adjoint eqations solution, gradient solution and quasi newton algorithm. The multigrid techniques are added to accelerate the convergence of flow and adjoint equations to improve the efficiency of design. Design examples including inverse problem and drag minimization are performed for transonic wing. The results indicate that the present method can be successfully applied to optimization design of transonic wing. Satisfactory designs are usually obtained with 20-30 design cycles.