A stabilized pseudo-shell approach for surface parametrization in CFD design problems.

*(English)*Zbl 1063.76058Summary: 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.

##### 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 |

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\textit{O. Soto} et al., Commun. Numer. Methods Eng. 18, No. 4, 251--258 (2002; Zbl 1063.76058)

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