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Mesh deformation using radial basis functions for gradient-based aerodynamic shape optimization
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. (Waves and Fluids)
2007 (English)In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 36, 1119-1136 p.Article in journal (Refereed) Published
Place, publisher, year, edition, pages
2007. Vol. 36, 1119-1136 p.
National Category
Computational Mathematics Computer Science
URN: urn:nbn:se:uu:diva-22158DOI: 10.1016/j.compfluid.2006.11.002ISI: 000246537700008OAI: oai:DiVA.org:uu-22158DiVA: diva2:49931
Design Optimization
Available from: 2007-04-16 Created: 2007-04-16 Last updated: 2014-09-03Bibliographically approved
In thesis
1. Numerical Methods for Aerodynamic Shape Optimization
Open this publication in new window or tab >>Numerical Methods for Aerodynamic Shape Optimization
2005 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Gradient-based aerodynamic shape optimization, based on Computational Fluid Dynamics analysis of the flow, is a method that can automatically improve designs of aircraft components. The prospect is to reduce a cost function that reflects aerodynamic performances.

When the shape is described by a large number of parameters, the calculation of one gradient of the cost function is only feasible by recourse to techniques that are derived from the theory of optimal control. In order to obtain the best computational efficiency, the so called adjoint method is applied here on the complete mapping, from the parameters of design to the values of the cost function. The mapping considered here includes the Euler equations for compressible flow discretized on unstructured meshes by a median-dual finite-volume scheme, the primal-to-dual mesh transformation, the mesh deformation, and the parameterization. The results of the present research concern the detailed derivations of expressions, equations, and algorithms that are necessary to calculate the gradient of the cost function. The discrete adjoint of the Euler equations and the exact dual-to-primal transformation of the gradient have been implemented for 2D and 3D applications in the code Edge, a program of Computational Fluid Dynamics used by Swedish industries.

Moreover, techniques are proposed here in the aim to further reduce the computational cost of aerodynamic shape optimization. For instance, an interpolation scheme is derived based on Radial Basis Functions that can execute the deformation of unstructured meshes faster than methods based on an elliptic equation.

In order to improve the accuracy of the shape, obtained by numerical optimization, a moving mesh adaptation scheme is realized based on a variable diffusivity equation of Winslow type. This adaptation has been successfully applied on a simple case of shape optimization involving a supersonic flow. An interpolation technique has been derived based on a mollifier in order to improve the convergence of the coupled mesh-flow equations entering the adaptive scheme.

The method of adjoint derived here has also been applied successfully when coupling the Euler equations with the boundary-layer and parabolized stability equations, with the aim to delay the laminar-to-turbulent transition of the flow. The delay of transition is an efficient way to reduce the drag due to viscosity at high Reynolds numbers.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2005. 34 p.
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 135
Computational Fluid Dynamics, shape optimization, adjoint equations, edge-based finite-volume method, moving mesh adaptation, radial basis functions, inviscid compressible flow, transition control
National Category
Computational Mathematics
Research subject
Numerical Analysis
urn:nbn:se:uu:diva-6252 (URN)91-554-6431-9 (ISBN)
Public defence
2006-01-20, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 10:15 (English)
Available from: 2005-12-28 Created: 2005-12-28 Last updated: 2014-09-03Bibliographically approved

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