Adjoint-based optimal variable stiffness mesh deformation strategy based on bi-elliptic equations |
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Authors: | Qiqi Wang Rui Hu |
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Affiliation: | Department of Aeronautics and Astronautics, MIT, Cambridge, MA 02139, U.S.A. |
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Abstract: | 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. |
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Keywords: | mesh deformation biharmonic equation adjoint method Sobolev gradient mesh optimization |
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