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

摘要

There are many recent advances in mesh deformation methods for computational fluid dynamics simulation in deforming geometries. We present a method of constructing dy namic 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 op timization 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 multi-scenario optimization procedure is performed to calculate the optimal stiffness coefficient field a"(x) for a priori unpredictable boundary movements.