Soto, O.; Löhner, R.; Yang, C. A stabilized pseudo-shell approach for surface parametrization in CFD design problems. (English) Zbl 1063.76058 Commun. Numer. Methods Eng. 18, No. 4, 251-258 (2002). Summary: We describe a surface representation for computational fluid dynamics (CFD) shape design problems. The surface representation is based on the solution of a simplified pseudo-shell problem on the surface to be optimized. A stabilized finite element formulation is used to perform this step. The methodology has the advantage of being completely independent of the CAD representation. Moreover, the user does not have to predefine any set of shape functions to parameterize the surface. The scheme uses a reasonable discretization of the surface to automatically build the shape deformation modes, by using the pseudo-shell approach and the design parameter positions. Almost every point of the surface grid can be chosen as design parameter, which leads to a very rich design space. Most of the design variables are chosen in an automatic way, which makes the scheme easy to use. Furthermore, the surface grid is not distorted through the design cycles which avoids remeshing procedures. An example is presented to demonstrate the proposed methodology. Cited in 4 Documents MSC: 76M10 Finite element methods applied to problems in fluid mechanics 65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs Keywords:shape optimization; stabilized finite element formulation PDF BibTeX XML Cite \textit{O. Soto} et al., Commun. Numer. Methods Eng. 18, No. 4, 251--258 (2002; Zbl 1063.76058) Full Text: DOI References: [1] Samareh J Geometry modeling and grid generation for design and optimization 1998 [2] Chiandussi, Shape variable definition with C0, C1 and C2 continuity functions, Computer Methods in Applied Mechanics and Engineering 188 pp 727– (2000) [3] Jameson A Optimum aerodynamic design using CFD and control theory 1995 [4] Codina, On stabilized finite element methods for linear systems of convection-diffusion-reaction equations, Computer Methods in Applied Mechanics and Engineering 188 pp 61– (2000) · Zbl 0973.76041 [5] Brezzi, Mixed and Hybrid Finite Element Methods (1991) · Zbl 0788.73002 · doi:10.1007/978-1-4612-3172-1 [6] Yang C Noblesse F Löhner R Practical hydrodynamic optimization of a wave cancellation multihull ship 2001 [7] Soto O Löhner R General methodologies for incompressible flow design problems 2001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.