Mesh Deformation Method Based on Dual Quaternions and Their Combination with Radial Basis Functions

Mesh deformation technique is commonly used in CFD simulations with moving boundaries because of its high efficiency and mesh consistency, whose deformed mesh quality and calculation costs have important impacts on accuracy and efficiency of the full simulation flow. For the purpose of orthogonality preservation and more efficient deformation, this paper introduces a new mesh deformation method based on dual quaternions and their combination with radial basis functions (RBFs). Firstly, the translational and rotational effects at the boundary points are measured in a uniform way using the dual quaternions. Then their total displacements are propagated to the corresponding volume points along the normal direction under the control of the decay function, which can preserve the orthogonality of the near-wall mesh. In order to expand the application scenarios, the above method and the RBF method are combined to cope with the points inside and outside the boundary layer respectively in topologically complex mesh. With valid handling for elements near the wall by dual quaternions, fewer support points are required compared to the pure RBF method in the whole domain, reducing the calculation costs and improving deformation efficiency greatly. Two typical test cases with different mesh features and deformation modes demonstrates the superiority of the proposed method in mesh quality and deformation efficiency.