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

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 ( m = u 2/ am, am 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 m (e( 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( 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