Unified fluid-structure interpolation and mesh motion using radial basis functions.

*(English)*Zbl 1159.74457Summary: 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.

##### MSC:

74S30 | Other numerical methods in solid mechanics (MSC2010) |

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |

##### Keywords:

radial basis functions; multivariate interpolation; compactly supported functions; aeroelasticity; fluid-structure interpolation; information transfer; flutter; mesh motion
PDF
BibTeX
XML
Cite

\textit{T. C. S. Rendall} and \textit{C. B. Allen}, Int. J. Numer. Methods Eng. 74, No. 10, 1519--1559 (2008; Zbl 1159.74457)

Full Text:
DOI

**OpenURL**

##### References:

[1] | Bendiksen, Proceedings of the Institute of Mechanical Engineers Part G: Journal of Aerospace Engineering 218 pp 157– (2004) |

[2] | Hubner, Computer Methods in Applied Mechanics and Engineering 193 pp 2087– (2004) |

[3] | Woodgate, Journal of Aircraft 42 pp 1005– (2005) |

[4] | . Calculation of the AGARD wing 445.6 flutter using Navier–Stokes aerodynamics. AIAA Paper No. AIAA-93-3476, 1993. |

[5] | Geuzaine, AIAA Journal 41 pp 363– (2003) |

[6] | . Aeroservoelastic computations in unsteady flow. AIAA Paper No. AIAA-2000-4226, 2000. |

[7] | , , . Investigation of flutter suppression by active control. AIAA Paper No. AIAA-2003-3510, 2003. |

[8] | Unsteady aerodynamic simulation by flight control system integration with structure-coupled CFD first year report. Technical Report AE046, University of Bristol, 2003. |

[9] | Taylor, The Aeronautical Journal 108 pp 389– (2004) |

[10] | Allen, International Journal for Numerical Methods in Engineering 64 pp 1628– (2005) |

[11] | Fast evaluation of radial basis functions: methods based on partition of Unity. Approximation Theory X: Wavelets, Splines, and Applications. Vanderbilt University Press: Nashville, TX, U.S.A., 2002; 473–483. · Zbl 1031.65022 |

[12] | Ahrem, Computer Modeling in Engineering and Sciences 12 pp 121– (2006) |

[13] | Scattered Data Approximation (1st edn). Cambridge University Press: Cambridge, 2005. |

[14] | , . Development of generic CFD-based aerodynamic optimisation tools for helicopter rotor blades. Twenty-fifth Applied Aerodynamics Conference, Miami, FL, 2007; AIAA Paper No. AIAA- 2007-3809. |

[15] | , . Notes on Numerical Fluid Mechanics and Multidisciplinary Design. Volume 81: Progress in Computational Flow–Structure Interaction (1st edn). Springer: Berlin, 2002. |

[16] | Goura, AIAA Journal 42 pp 312– (2003) |

[17] | Cebral, AIAA Journal 35 pp 687– (1997) |

[18] | Maman, Computers and Structures 54 pp 779– (1995) |

[19] | , . A conservative mesh-free approach for fluid–structure interface problems. International Conference on Computational Methods for Coupled Problems in Science and Engineering, Barcelona, 2005. |

[20] | Schmitt, Journal of the Aeronautical Sciences pp 980– (1956) |

[21] | Jiao, International Journal for Numerical Methods in Engineering 61 pp 2402– (2004) |

[22] | Pidparti, Journal of Aircraft 29 pp 507– (1992) |

[23] | Discrete data transfer technique for fluid–structure interaction. AIAA Paper No. AIAA-2007-4309, 2007. |

[24] | A unified approach to modeling multidisciplinary interactions. AIAA Paper No. AIAA-2000-4704, 2000. |

[25] | Force transfer in aeroelastic calculations. Technical Report, Bristol University Aerospace Department, December 2002. |

[26] | Goura, The Aeronautical Journal 105 pp 215– (2001) |

[27] | Chen, AIAA Journal 36 pp 282– (1998) |

[28] | Jiao, International Journal of Computational Geometry and Applications 14 pp 379– (2004) |

[29] | , , . Application of three-dimensional interfaces for data transfer in aeroelastic applications. AIAA Paper No. AIAA-2004-5376, 2004. |

[30] | . Coupled fluid–structure simulation for turbomachinery blade rows. AIAA Paper No. AIAA-2005-0018, 2005. |

[31] | Assessment of inter-grid transformation for complete aircraft aeroelastic analysis. Master’s Thesis, University of Glasgow, 2002. |

[32] | Allen, The Aeronautical Journal 106 pp 559– (2002) |

[33] | Jones, CFD Journal, Japanese Society of CFD pp 430– (2001) |

[34] | Batina, AIAA Journal 29 pp 327– (1991) |

[35] | , . Dynamic unstructured method for flows past multiple objects in relative motion. AIAA Paper No. AIAA-94-0058, 1994. |

[36] | Farhat, Computer Methods in Applied Mechanics and Engineering 163 pp 231– (1998) |

[37] | Blom, International Journal for Numerical Methods in Fluids 32 pp 647– (2000) |

[38] | , . Solid brick analogy for automatic grid deformation for fluid–structure interaction. AIAA Paper No. AIAA-2006-3219, 2006. |

[39] | Loehner, Communications in Numerical Methods in Engineering 12 pp 599– (1996) |

[40] | , , , . Application of unstructured moving body methodology to the simulation of fuel tank separation from an F-16 fighter. AIAA Paper No. AIAA-1997-0166, 1997. |

[41] | Grid deformation of 3D hybrid grids. Proceedings of the 8th International Conference on Numerical Grid Generation in Computational Field Simulations, Greenwich, 2002. |

[42] | Helenbrook, International Journal for Numerical Methods in Engineering 56 pp 1007– (2003) |

[43] | Nonlinear simulation of F-16 aeroelastic instability. AIAA Paper No. AIAA-2001-0570, 2001. |

[44] | Dynamic aeroelastic simulation of complex configurations using overset grid systems. AIAA Paper No. AIAA-2000-2341, 2000. |

[45] | Allen, International Journal for Numerical Methods in Engineering 69 pp 2126– (2007) |

[46] | . Mesh generation and deformation algorithm for aeroelasticity simulations. Forty-fifth Aerospace Sciences Meeting, Reno, NV, 2007; AIAA Paper No. AIAA-2007-556. |

[47] | Liu, Journal of Computational Physics 211 pp 405– (2006) |

[48] | Beckert, Aerospace Science and Technology 5 pp 125– (2001) |

[49] | , . Comparing different methods for the coupling of non-matching meshes in fluid–structure interaction computations. AIAA Paper No. AIAA-2005-4620, 2005. |

[50] | Radial Basis Functions (1st edn). Cambridge University Press: Cambridge, 2005. |

[51] | Harder, Journal of Aircraft 9 pp 189– (1972) |

[52] | , . An evaluation of computational algorithms to interface between CFD and CSD methodologies. Technical Report WL-TR-96-3055, Wright Laboratory, November 1995. |

[53] | , . A simple, robust and fast algorithm to compute deformations of multiblock structured grids. Technical Report NLR-TP-2002-105, NLR, 2002. |

[54] | . Evaluation of elastomechanical and aerodynamic data transfer methods for non-planar configurations in computational aeroelastic analysis. Technical Report NLR-TP-95690U, NLR, 1994. |

[55] | . Transonic static aeroelastic simulations of a fighter aircraft. Technical Report NLR-TP-2003-187, NLR, 2003. |

[56] | de Boer, Computers and Structures 85 pp 784– (2007) |

[57] | van Zuijlen, Journal of Computational Physics 224 pp 414– (2007) |

[58] | . Mesh deformation using radial basis functions for gradient based aerodynamic shape optimization. Technical Report FOI-R-1784-SE, FOI, December 2005. |

[59] | Multi-discipline optimisation in preliminary design of commercial transport aircraft. In Computational Methods in Applied Sciences, ECCOMAS, , , , , , (eds). Wiley: New York, 1996; 523–526. |

[60] | Allen, International Journal for Numerical Methods in Fluids 39 pp 121– (2002) |

[61] | Flux Vector Splitting for the Euler Equations. Lecture Notes in Physics, vol. 170. Springer: Berlin, 1982; 507–512. |

[62] | Parpia, AIAA Journal 26 pp 113– (1988) |

[63] | Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings. AIAA Paper No. AIAA-1991-1596, 1991. |

[64] | . Fully implicit time-marching aeroelastic solutions. AIAA Paper No. AIAA-1994-0056, 1994. |

[65] | Allen, International Journal for Numerical Methods in Engineering (2007) |

[66] | . Grid generation using a posteriori optimization with geometrically normalised functions. Applied Aerodynamics Conference, Portland, OR, 1990; AIAA Paper No. AIAA-1990-3048. |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.