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A numerical methodology to assess the quality of the design velocity field computation methods in shape sensitivity analysis

机译：评估形状灵敏度分析中设计速度场计算方法质量的数值方法

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摘要

The velocity field in shape sensitivity analysis is not uniquely defined although it must meet numerous theoretical and practical criteria. These practical criteria can be used to compare the existing velocity field computation methods which meet the theoretical criteria, but only in qualitative terms. When the FEM is used in design sensitivity analysis (DSA), due to the FE discretization error, the DSA errors will depend on the design velocity field considered. This paper presents a numerical methodology for quality evaluation of design velocity field computation methods in quantitative terms based on the analysis of the DSA discretization error. The sensitivity of the squared energy norm (X_m = partiv deriv‖u‖~2/partial deriva_m, a_m being a design variable) has been taken as the magnitude to measure the error of the DSA. For h-refinements, the squared error in energy norm (‖e(u)‖~2) and the error in X_m (e(X_m)) are theoretically related by a constant which is independent of the refinement degree of the FE model. The quality of the design velocity field computation methods can therefore be assessed in terms of the stability of e(X_m/‖e(u)‖~2 in sequences of meshes. An example of the use of this methodology, where six design velocity field computation methods are compared, is presented.
机译：尽管形状灵敏度分析中的速度场必须满足许多理论和实践标准，但并没有唯一定义。这些实用准则可用于比较满足理论准则的现有速度场计算方法，但仅限于定性方面。当FEM用于设计灵敏度分析（DSA）时，由于FE离散误差，DSA误差将取决于所考虑的设计速度场。本文在分析DSA离散化误差的基础上，提出了一种定量评估设计速度场计算方法质量的数值方法。以能量平方平方的灵敏度（X_m =偏导u_〜2 /偏deriva_m，a_m为设计变量）作为测量DSA误差的大小。对于h细化，理论上能量范数的平方误差（“ e（u）”〜2）和X_m的误差（e（X_m））在理论上由一个常数构成，该常数与有限元模型的细化程度无关。因此，可以根据网格序列中e（X_m /‖e（u）‖〜2的稳定性来评估设计速度场计算方法的质量，该方法的使用示例是六个设计速度场比较计算方法，介绍。

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