High-Quality Mesh Deformation Using Quaternions for Orthogonality Preservation

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 met...

[1]  J. Batina.  UNSTEADY EULER ALGORITHM WITH UNSTRUCTURED DYNAMIC MESH FOR COMPLEX – AIRCRAFT AERODYNAMIC ANALYSIS , 1991 .

[2]  H. Jasak,et al.  Automatic mesh motion for the unstructured finite volume method , 2007 .

[3]  Ken Shoemake,et al.  Animating rotation with quaternion curves , 1985, SIGGRAPH.

[4]  Jamshid A. Samareh,et al.  Application of Quaternions for Mesh Deformation , 2002 .

[5]  C. Farhat,et al.  Torsional springs for two-dimensional dynamic unstructured fluid meshes , 1998 .

[6]  Timothy J. Baker,et al.  Mesh Movement and Metamorphosis , 2002, Engineering with Computers.

[7]  Sam Lee,et al.  Effect of High-Fidelity Ice-Accretion Simulations on Full-Scale Airfoil Performance , 2010 .

[8]  H. Bijl,et al.  Mesh deformation based on radial basis function interpolation , 2007 .

[9]  M. Meaux,et al.  VISCOUS AERODYNAMIC SHAPE OPTIMIZATION BASED ON THE DISCRETE ADJOINT STATE FOR 3D INDUSTRIAL CONFIGURATIONS , 2004 .

[10]  Marc Alexa,et al.  Linear combination of transformations , 2002, ACM Trans. Graph..

[11]  Brian T. Helenbrook,et al.  Mesh deformation using the biharmonic operator , 2003 .

[12]  David Martineau,et al.  A Mesh Movement Algorithm for High Quality Generalised Meshes , 2004 .

[13]  K. Kovalev,et al.  Unstructured Hexahedral Non-conformal Mesh Generation , 2005 .

[14]  A. Przekwas,et al.  Unsteady flow computation using moving grid with mesh enrichment , 1994 .

[15]  Paul G. A. Cizmas,et al.  Mesh Generation and Deformation Algorithm for Aeroelasticity Simulations , 2007 .

[16]  Laurent Cambier,et al.  Status of the elsA CFD Software for Flow Simulation and Multidisciplinary Applications , 2008 .

[17]  Erik B. Dam,et al.  Quaternions, Interpolation and Animation , 2000 .

[18]  F. Blom.  Considerations on the spring analogy , 2000 .

[19]  Christian B Allen,et al.  Parallel universal approach to mesh motion and application to rotors in forward flight , 2007 .

[20]  ShoemakeKen.  Animating rotation with quaternion curves , 1985 .

[21]  Oddvar O. Bendiksen,et al.  Unsteady Transonic Two-Dimensional Euler Solutions Using Finite Elements , 1993 .

[22]  F. Sebastian Grassia,et al.  Practical Parameterization of Rotations Using the Exponential Map , 1998, J. Graphics, GPU, & Game Tools.

[23]  C. Allen,et al.  Unified fluid–structure interpolation and mesh motion using radial basis functions , 2008 .