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基于自主研发的大规模并行化结构化网格RANS求解器PMB3D,开展了黏性离散伴随方程构造、求解方法的研究与讨论。首先对离散伴随求解梯度的思想进行简要介绍,进一步对无黏项、人工黏性项、黏性项部分对离散伴随方程贡献以及变分推导进行了详细介绍;文中对离散伴随方程无黏项、黏性项边界条件实现形式进行了详细研究,并对关键模块变分推导的一些简化方式进行了研究讨论,通过典型宽体飞机标模、外压式超声速进气道算例,分析了所采用的简化处理方式对不同问题梯度求解精度的影响。最后在并行化求解、时间推进以及加速收敛方面进行了探讨、验证。数值模拟表明,文中采用的离散伴随方程形式更有利于程序化、模块化,梯度计算精度完全满足气动优化设计需要。
Based on the massively parallel RANS solver PMB3D developed independently, a research and discussion on the construction and solution of viscous discrete adjoint equations are carried out. Firstly, the concept of discrete adjoint solving gradient is introduced briefly, and the contribution of discrete adjoint equation and variational derivation are further described in detail. In the paper, the discrete adjoint equation has no sticky item, Some forms of simplifying the derivative derivation of the key modules are discussed and discussed. Based on the typical examples of wide-body aircraft supersonic supersonic air inlets and examples, The Influence of Simplified Processing Methods on the Resolution Accuracy of Different Problems. Finally, we discuss and verify the parallel solution, time advancement and acceleration convergence. Numerical simulation shows that the discrete adjoint equation used in this paper is more conducive to program and modularization, and the accuracy of gradient calculation can fully meet the needs of aerodynamic optimization design.