New Hybrid Interpolation Method for Motion Transfer in Fluid-Structure Interactions

Abstract

Introduction I N computational aeroelastic analyses by loosely coupled approaches, efficient and accurate interpolation is essential to transfer structural deformation to aerodynamic grid points due to the intrinsically different resolution in fluid and structural grids. The numerous interpolation methods used in motion transfer can be categorized into two groups: surface spline and tracking methods. The surface spline methods solve a linear equation consisting of radial basis functions to obtain a globally representative surface. For example, these methods employ infinite plate spline1 (IPS), thin plate spline2 (TPS), and multiquadrics3 (MQ). IPS is widely used because of its simplicity and smoothness. The system matrices from these methods are prone to becoming ill conditioned when used with unstructured grids and large numbers of nodes. A subdomaining approach has been applied to TPS and MQ to reduce this instability.4 The tracking methods use the natural coordinates of fluid nodes projected to nearest structural elements. The accuracy of these methods is low at highly curved geometries. Several algorithms such as quadratic interpolation, initial distance vectors, and rotated distance vectors with point normals have been suggested to increase accuracy.5 In this study, a new hybrid interpolation method, referred to as curvature gradient index local fitting (CILF), is suggested. CILF uses a surface spline method at local geometries having high curvature gradient and a tracking method at the remaining geometries. Analytical test cases and motion transfer of an AGARD 445.6 wing6 are implemented to show efficiency, accuracy, and smoothness of the suggested method in comparison with other interpolation methods.