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

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.

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