Adjoint-based optimal variable stiffness mesh deformation strategy based on bi-elliptic equations

作者：Wang Qiqi^*; Hu Rui

来源：International Journal for Numerical Methods in Engineering, 2012, 90(5): 659-670.

DOI：10.1002/nme.3341

• mesh deformation
• biharmonic equation
• adjoint method
• Sobolev gradient
• mesh optimization

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?(x) for a priori unpredictable boundary movements.

• 出版日期2012-5-4
• 单位MIT