Integrated improvement of the elasticity-based mesh deformation method based on robust parameters and mesh quality

Abstract

Highly robust mesh deformation methods are key techniques for solving unsteady flow field problems with moving or deforming boundaries. Because it is imperative to reduce the remeshing times, these methods are important in engineering applications, especially for complex geometric boundaries and large displacements. We introduce three classical elasticity-based mesh deformation methods and determine the limitations of the two nonlinear classical methods. Two steps were taken to achieve an integrated improvement: first, the robust power parameters a and b and the weighted parameter x are introduced to enhance the robustness of the basic elasticity equation. Second, a mesh quality parameter is implemented to prevent the large distortion of the poor elements and this parameter is added to the elasticity equation as a constraint. To validate the validity of the integrated improvement approach, several test cases of a moving or deforming two-dimensional flat plate are used. Additionally, two simulated engineering examples are used to demonstrate the application of the integrated improvement for practical problems, including the pitching oscillation of a National Advisory Committee for Aeronautics (NACA) 0012 airfoil and the ONERA M6 wing. The results show that the integrated improvement approach does not only allow for the selection of suitable robust parameters to achieve more robust deformed meshes but also reduces the distortion of the poor elements near the moving boundary, even when the deformation is severe.