并行的多重网格方法在离散伴随优化中的应用

Application of Parallel Multigrid Algorithm to Discrete Adjoint Optimization

伴随优化方法在飞行器气动外形优化设计方面的应用越来越广泛,但以精细减阻等为目标的优化,面对真实飞行器仍然存在计算量大、计算周期长的问题。将多重网格技术结合并行技术运用于基于非结构混合网格、雷诺平均Navier-Stokes方程的离散伴随方程的求解,提高了离散伴随优化系统的整体效率。给出了伴随方程多重网格计算中的延拓和限制算子,采用V循环比较了不同层数的加速效果和粗网格残差计算方法对目标函数梯度敏感导数的影响。结合Metis分区技术,提出了适合伴随方程的数据并行传递简化方式,使伴随方程在300个并行分区计算时加速比仅比理想加速比低13%。采用发展的高效优化系统,选取了112个设计变量,对DLR F6翼身组合体跨声速状态进行减阻优化,使机翼空间激波得到弱化,阻力减小9counts。模拟验证结果表明,建立的高效的飞行器气动外形优化设计系统在三维真实飞行器外形优化方面,具有良好的应用前景。

The adjoint method is now employed more and more widely for aerodynamic shape optimization.But when used for reducing the drag of a complex aircraft,it still requires a large amount of time-consuming calculation.Based on an unstructured mesh,this paper proposes a parallel multigrid algorithm to solve the discrete adjoint equation for a 3D Reynoldsaveraged Navier-Stokes solver,so as to improve the optimization system efficiency.The prolongation operator and the restriction operator are described for the multigrid adjoint solver.By using the V-cycle,the accelerating effect of different layers is compared,and the influence of coarse grid residuals computing methods on the gradient of the objective function is analyzed.Combined with Metis partitioning technology,a simplified parallel-data transfer approach is implemented for the adjoint solver,so that the parallel speedup of the adjoint equation is only 13％ lower than the ideal speedup in 300 parallel partitions.The optimization system is successfully demonstrated for a DLR F6 wing-body transonic shape optimization design,in which 112 design variables are selected with the purpose of reducing drag.Shock structure change is presented before and after the optimization,and drag reduction is nine counts.It shows that the efficient optimization system established in this paper has a bright application prospect for three-dimensional complex shape optimization.