High-Quality Mesh Deformation Using Quaternions for Orthogonality Preservation

Abstract

Many mesh deformation techniques developed in the past have been widely used, but for large deformations, the mesh properties can be severely altered. In particular, the mesh lines orthogonality near the boundaries can be lost. In this paper, a method initially proposed by Samareh (“Application of Quaternions for Mesh Deformation,” NASA TM-2002-211646, April 2002) is developed to overcome this limitation and to provide a high-quality mesh-orthogonality preservation technique. Each node displacement is composed of a translation vector and a quaternion, which takes into account local mesh rotations. Algebraic unitary quaternion properties (Lie group algebra) are used to obtain a robust interpolation method. Two quaternion interpolation methods are compared, respectively: the spherical linear interpolation, and the Lie algebra linear interpolation. Furthermore, thanks to a new process (transformation division), the method becomes independent of the rotation center used. The accuracy and generality of the method is significantly improved by this new process, and different test cases (two-dimensional and three-dimensional) are presented to illustrate the benefits obtained. Global mesh quality is shown to be preserved, especially local mesh orthogonality near the moving surfaces. The application to an iced airfoil shows the capability of the method to propagate very severe deformations while providing deformed mesh that enables accurate Reynolds-averaged Navier–Stokes computational fluid dynamics calculations.