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RBF-based mesh morphing improvement using Schur complement applied to rib shape optimization

Franck Mastrippolito (Univ. Lyon, Ecole Centrale de Lyon, Laboratoire de Mécanique des Fluides et d'Acoustique UMR5509, Ecully, France and Univ. Grenoble Alpes, CEA, LITEN, DTBH, Laboratoire Echangeurs et Réacteurs, Grenoble, France)
Stephane Aubert (Univ. Lyon, Ecole Centrale de Lyon, Laboratoire de Mécanique des Fluides et d'Acoustique UMR5509, Ecully, France)
Frédéric Ducros (Univ. Grenoble Alpes, CEA, LITEN, DTBH, Laboratoire Echangeurs et Réacteurs, Grenoble, France)
Martin Buisson (Univ. Lyon, Ecole Centrale de Lyon, Laboratoire de Mécanique des Fluides et d'Acoustique UMR5509, Ecully, France)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 28 August 2019

Issue publication date: 20 August 2020

Abstract

Purpose

This paper aims to improve the radial basis fuction mesh morphing method. During a shape optimization based on computational fluid dynamic (CFD) solvers, the mesh has to be changed. Two possible strategies are re-meshing or morphing. The morphing one is advantageous because it preserves the mesh connectivity, but it must be constrained.

Design/methodology/approach

RBF mesh deformation is one of the most robust and accurate morphing method. Using a greedy algorithm, the computational cost of the method is reduced. To evaluate the morphing performances, a rib shape optimization is performed using the NSGA-II algorithm coupled to kriging metamodels based on CFD. The morphing method is then compared to a re-meshing strategy.

Findings

The authors propose a method, based on Schur complement, to speed-up the greedy process. By using the information of the previous iteration, smaller linear systems are solved and time is saved. The optimization results highlight the interest of using a morphing-based metamodel regarding the resolution time and the accuracy of the interpolated solutions.

Originality/value

A new method based on Schur complement is addressed to speed-up the greedy algorithm and successfully applied to a shape optimization.

Keywords

Citation

Mastrippolito, F., Aubert, S., Ducros, F. and Buisson, M. (2020), "RBF-based mesh morphing improvement using Schur complement applied to rib shape optimization", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 30 No. 9, pp. 4241-4257. https://doi.org/10.1108/HFF-06-2018-0309

Publisher

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Emerald Publishing Limited

Copyright © 2019, Emerald Publishing Limited