Unified fluid–structure interpolation and mesh motion using radial basis functions

A multivariate interpolation scheme, using radial basis functions, is presented, which results in a completely unified formulation for the fluid–structure interpolation and mesh motion problems. The method has several significant advantages. Primarily, all volume mesh, structural mesh, and flow‐solver type dependence is removed, and all operations are performed on totally arbitrary point clouds of any form. Hence, all connectivity and user‐input requirements are removed from the computational fluid dynamics–computational structural dynamics (CFD–CSD) coupling problem, as only point clouds are required to determine the coupling. Also, it may equally well be applied to structured and unstructured grids, or structural and aerodynamic grids that intersect, again because no connectivity information is required. Furthermore, no expensive computations are required during an unsteady simulation, just matrix–vector multiplications, since the required dependence relations are computed only once prior to any simulation and then remain constant. This property means that the method is both perfectly parallel, since only the data relevant to each structured block or unstructured partition are required to move those points, and totally independent from the flow solver. Hence, a completely generic ‘black box’ tool can be developed, which is ideal for use in an optimization approach. Aeroelastic behaviour of the Brite–Euram MDO wing is analysed in terms of both static deflection and dynamic responses, and it is demonstrated that responses are strongly dependent on the exact CFD–CSD interpolation used. Mesh quality is also examined during the motion resulting from a large surface deformation. Global grid quality is shown to be preserved well, with local grid orthogonality also being maintained well, particularly at and near the moving surface, where the original orthogonality is retained. Copyright © 2007 John Wiley & Sons, Ltd.

[1]  R. N. Desmarais,et al.  Interpolation using surface splines. , 1972 .

[2]  Ijaz H. Parpia,et al.  van Leer flux vector splitting in moving coordinates , 1988 .

[3]  A. Jameson.  Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings , 1991 .

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

[5]  R. Pidaparti,et al.  Structural and aerodynamic data transformation using inverse isoparametric mapping , 1992 .

[6]  M Lee Elizabeth,et al.  Calculation of AGARD Wing 445.6 Flutter Using Navier-Stokes Aerodynamics , 1993 .

[7]  Juan J. Alonso,et al.  Fully-implicit time-marching aeroelastic solutions , 1994 .

[8]  Oktay Baysal,et al.  Dynamic unstructured method for flows past multiple objects in relative motion , 1995 .

[9]  Charbel Farhat,et al.  Matching fluid and structure meshes for aeroelastic computations : a parallel approach , 1995 .

[10]  Marilyn J. Smith,et al.  An Evaluation of Computational Algorithms to Interface Between CFD and CSD Methodologies. , 1996 .

[11]  Rainald Löhner,et al.  Improved ALE mesh velocities for moving bodies , 1996 .

[12]  Rainald Loehner,et al.  Application of unstructured adaptive moving body methodology to the simulation of fuel tank separation from an F-16 fighter , 1997 .

[13]  Rainald Löhner,et al.  Conservative load projection and tracking for fluid-structure problems , 1996 .

[14]  B. Leer,et al.  Flux-vector splitting for the Euler equations , 1997 .

[15]  I. Jadic,et al.  Interfacing of Fluid and Structural Models via Innovative Structural Boundary Element Method , 1998 .

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

[17]  Reid Melville,et al.  Dynamic aeroelastic simulation of complex configurations using overset grid systems , 2000 .

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

[19]  A Samareh Jamshid,et al.  A Unified Approach to Modeling Multidisciplinary Interactions , 2000 .

[20]  Reid Melville.  Nonlinear simulation of F-16 aeroelastic instability , 2001 .

[21]  H. Wendland,et al.  Multivariate interpolation for fluid-structure-interaction problems using radial basis functions , 2001 .

[22]  Bryan E. Richards,et al.  A data exchange method for fluid-structure interaction problems , 2001 .

[23]  Christian B Allen,et al.  Multigrid convergence of inviscid fixed‐ and rotary‐wing flows , 2002 .

[24]  Cb Allen.  Aeroelastic computations using algebraic grid motion , 2002 .

[25]  Charbel Farhat,et al.  Aeroelastic Dynamic Analysis of a Full F-16 Configuration for Various Flight Conditions , 2003 .

[26]  Christian B Allen,et al.  Investigation of flutter suppression by active control , 2003 .

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

[28]  Ken Badcock,et al.  Extrapolation effects on coupled computational fluid dynamics/computational structural dynamics simulations , 2003 .

[29]  O O Bendiksen,et al.  Modern developments in computational aeroelasticity , 2004 .

[30]  Michael T. Heath,et al.  Overlaying surface meshes, part I: algorithms , 2004, Int. J. Comput. Geom. Appl..

[31]  Michael T. Heath,et al.  Common‐refinement‐based data transfer between non‐matching meshes in multiphysics simulations , 2004 .

[32]  D. Dinkler,et al.  A monolithic approach to fluid–structure interaction using space–time finite elements , 2004 .

[33]  Christian B Allen,et al.  A structure-coupled CFD method for time-marching flutter analysis , 2004, The Aeronautical Journal (1968).

[34]  Kwok Leung Lai,et al.  Application of Three-Dimensional Interfaces for Data Transfer in Aeroelastic Computations , 2004 .

[35]  Mani Sadeghi,et al.  Coupled Fluid-Structure Simulation for Turbomachinery Blade Rows , 2005 .

[36]  P. Mantegazza,et al.  A Conservative Mesh-Free Approach for Fluid Structure Interface Problems , 2005 .

[37]  Ken Badcock,et al.  Aeroelastic calculations for the hawk aircraft using the euler equations , 2005 .

[38]  Hester Bijl,et al.  Comparing Different Methods for the Coupling of Non-Matching Meshes in Fluid-Structure Interaction Computations , 2005 .

[39]  Christian B Allen,et al.  A comparison of full non-linear and reduced order aerodynamic models in control law design using a two-dimensional aerofoil model , 2005 .

[40]  Regine Ahrem,et al.  A Meshless Spatial Coupling Scheme for Large-scale Fluid-structure-interaction Problems , 2006 .

[41]  Ning Qin,et al.  Fast dynamic grid deformation based on Delaunay graph mapping , 2006 .

[42]  O. Amoignon,et al.  Mesh Deformation using Radial Basis Functions for Gradient-based Aerodynamic Shape Optimization , 2007 .

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

[44]  Hester Bijl,et al.  Higher-order time integration through smooth mesh deformation for 3D fluid-structure interaction simulations , 2007, J. Comput. Phys..

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

[46]  Thomas Rendall,et al.  Development of Generic CFD-Based Aerodynamic Optimisation Tools for Helicopter Rotor Blades , 2007 .