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

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.