Abstract
SUMMARYThere 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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