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Adjoint‐based optimal variable stiffness mesh deformation strategy based on bi‐elliptic equations
Author(s) -
Wang Qiqi,
Hu Rui
Publication year - 2011
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3341
Subject(s) - biharmonic equation , mathematics , stiffness , sobolev space , boundary (topology) , mathematical analysis , deformation (meteorology) , boundary value problem , physics , structural engineering , engineering , meteorology
SUMMARY There are many recent advances in mesh deformation methods for computational fluid dynamics simulation in deforming geometries. We present a method of constructing dynamic mesh around deforming objects by solving the bi‐elliptic equation, an extension of the biharmonic equation. We show that introducing a stiffness coefficient field a ( x ) in the bi‐elliptic equation can enable mesh deformation for very large boundary movements. An indicator of the mesh quality is constructed as an objective function of a numerical optimization procedure to find the best stiffness coefficient field a ( x ). The optimization is efficiently solved using steepest descent along adjoint‐based, integrated Sobolev gradients. A multiscenario optimization procedure is performed to calculate the optimal stiffness coefficient field a 蜧 ( x ) for a priori unpredictable boundary movements. Copyright © 2011 John Wiley & Sons, Ltd.