Skip to main content
SpringerLink
Log in

Radial Basis Functions for Interface Interpolation and Mesh Deformation

  • Conference paper
  • First Online:
Advanced Computational Methods in Science and Engineering

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 71))

Abstract

Many engineering applications involve fluid-structure interaction (FSI) phenomena. For instance light-weight airplanes, long span suspension bridges and modern wind turbines are susceptible to dynamic instability due to aeroelastic effects. FSI simulations are crucial for an efficient and safe design. Computers and numerical algorithms have significantly advanced over the last decade, such that the simulation of these problems has become feasible.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ahrem, R., Beckert, A., Wendland, H.: A new multivariate interpolation method for large-scale coupling problems in aeroelasticity. Conference proceedings IFADS, Munich (2005)

    Google Scholar 

  2. Batina, J.T.: Unsteady Euler algorithm with unstructured dynamic mesh for complex-aircraft aeroelastic analysis. Tech. Rep. AIAA-89-1189 (1989)

    Google Scholar 

  3. Beckert, A., Wendland, H.: Multivariate interpolation for fluid-structure-interaction problems using radial basis functions. Aerospace Science and Technology 5(2), 125–134 (2001)

    Article  MATH  Google Scholar 

  4. Bijl, H., Carpenter, M.H.: Iterative solution techniques for unsteady flow computations using higher order time integration schemes. International Journal for Numerical Methods in Fluids 47(8–9), 857–862 (2005)

    Article  MATH  Google Scholar 

  5. Bijl, H., Carpenter, M.H., Vatsa, V.N., Kennedy, C.A.: Implicit time integration schemes for the unsteady compressible Navier-Stokes equations: Laminar flow. Journal of Computational Physics 179, 313–329 (2002)

    Article  MATH  Google Scholar 

  6. Billings, S.D., Beatson, R.K., Newsam, G.N.: Interpolation of geophysical data with continuous global surfaces. Geophysics 67, 1810–1822 (2002)

    Article  Google Scholar 

  7. Billings, S.D., Newsam, G.N., Beatson, R.K.: Smooth fitting of geophysical data with continuous global surfaces. Geophysics 67, 1823–1834 (2002)

    Article  Google Scholar 

  8. Blom, F.J.: Considerations on the spring analogy. International Journal for Numerical Methods in Fluids 32, 647–668 (2000)

    Article  MATH  Google Scholar 

  9. de Boer, A., van der Schoot, M.S., Bijl, H.: Mesh deformation based on radial basis function interpolation. Computers and Structures 85(11—14), 784–795 (2007)

    Article  Google Scholar 

  10. de Boer, A., van Zuijlen, A.H., Bijl, H.: Review of coupling methods for non-matching meshes. Computer Methods in Applied Mechanics and Engineering 196(8), 1515–1525 (2006)

    Article  MathSciNet  Google Scholar 

  11. Buhmann, M.D.: Radial basis functions. Acta Numerica 9, 1–38 (2000)

    Article  MathSciNet  Google Scholar 

  12. Carr, J.C., Beatson, R.K., McCallum, B.C., Fright, W.R., McLennan, T.J., Mitchell, T.J.: Smooth surface reconstruction from noisy range data. First International Conference on Computer Graphics and Interactive Techniques (2003)

    Google Scholar 

  13. Cebral, J.R., Löhner, R.: Conservative load projection and tracking for fluid-structure problems. AIAA Journal 35(4), 687–692 (1997)

    Article  MATH  Google Scholar 

  14. Degand, C., Farhat, C.: A three-dimensional torsional spring analogy method for unstructured dynamic meshes. Computers and Structures 80, 305–316 (2002)

    Article  Google Scholar 

  15. Farhat, C., Degrand, C., Koobus, B., Lesoinne, M.: Torsional springs for two-dimensional dynamic unstructured fluid meshes. Computer Methods in Applied Mechanics and Engineering 163, 231–245 (1998)

    Article  MATH  Google Scholar 

  16. Farhat, C., Géradin, M.: On a component mode synthesis method and its application to incompatible substructures. Computers and Structures 51, 459–473 (1994)

    Article  MATH  Google Scholar 

  17. Farhat, C., Lesoinne, M., Tallec, P.: Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: Momentum and energy conservation, optimal discretization and application to aeroelasticity. Computer Methods in Applied Mechanics and Engineering 157, 95–114 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  18. Felippa, C.A., Park, K.C., Farhat, C.: Partitioned analysis of coupled mechanical systems. Computer Methods in Applied Mechanics and Engineering 190, 3247–3270 (2001)

    Article  MATH  Google Scholar 

  19. Gravouil, A., Combescure, A.: Multi-time-step explicit-implicit method for non-linear structural dynamics. International Journal for Numerical Methods in Engineering 50(1), 199–225 (2001)

    Article  MATH  Google Scholar 

  20. Heinstein, M.W., Laursen, T.A.: A three dimensional surface-to-surface projection algorithm for non-coincident domains. Communications in Numerical Methods in Engineering 19, 421–432 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  21. Helenbrook, B.T.: Mesh deformation using the biharmonic operator. International Journal for Numerical Methods in Engineering 56, 1007–1021 (2003)

    Article  MATH  Google Scholar 

  22. Kansa, E.J.: Multiquadrics – a scattered data approximation scheme with applications to computational fluid-dynamics – I: Surface approximations and partial derivative estimates. Computers & Mathematics with Applications 19, 127–145 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  23. Kansa, E.J.: Multiquadrics – a scattered data approximation scheme with applications to computational fluid-dynamics – II: Solutions to parabolic, hyperbolic and elliptic partial differential equations. Computers & Mathematics with Applications 19, 147–161 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  24. Kee, B.B.T., Liua, G.R., Zhanga, G.Y., Luc, C.: A residual based error estimator using radial basis functions. Finite Elements in Analysis and Design 44(9–10), 139–181 (2008)

    Google Scholar 

  25. Knupp, P.M.: Algebraic mesh quality metrics for unstructured initial meshes. Finite Elements in Analysis and Design 39, 217–241 (2003)

    Article  MATH  Google Scholar 

  26. Kovalev, K.: Unstructured hexahedral non-conformal mesh generation. Ph.D. thesis, Vrije Universiteit Brussel (2005)

    Google Scholar 

  27. Löhner, R., Yang, C., Cebral, J., Baum, J.D., Luo, H., Pelessone, D., Charman, C.: Fluid-structure interaction using a loose coupling algorithm and adaptive unstructured grids. In: M. Hafez, K. Oshima (eds.) Computational Fluid Dynamics Review. John Wiley (1995)

    Google Scholar 

  28. Lynch, D., ONeill, K.: Elastic grid deformation for moving boundary problems in two space dimensions. In: S. Wang (ed.) Finite Elements in Water Resources (1980)

    Google Scholar 

  29. Maman, N., Farhat, C.: Matching fluid and structure meshes for aeroelastic computations: A parallel approach. Computers and Structures 54(4), 779–785 (1995)

    Article  Google Scholar 

  30. Potsdam, M.A., Guruswamy, G.P.: A parallel multiblock mesh movement scheme for complex aeroelastic applications. Tech. Rep. AIAA-2001–0716 (2001)

    Google Scholar 

  31. Smith, M.J., Cesnik, C.E.S., Hodges, D.H.: Evaluation of some data transfer algorithms for noncontiguous meshes. Journal of Aerospace Engineering 13(2), 52–58 (2000)

    Article  Google Scholar 

  32. Smith, M.J., Hodges, D.H., Cesnik, C.E.S.: Evaluation of computational algorithms suitable for fluid-structure interactions. Journal of Aircraft 37(2), 282–294 (2000)

    Article  Google Scholar 

  33. Spekreijse, S., Prananta, B., Kok, J.: A simple, robust and fast algorithm to compute deformations of multi-block structured grids. Tech. rep. (2002)

    Google Scholar 

  34. Thévenza, P., Blu, T., Unser, M.: Interpolation revisited. IEEE Transactions on Medical Imaging 19(7), 739–758 (2000)

    Article  Google Scholar 

  35. Wang, Z.J., Przekwas, A.J.: Unsteady flow computation using moving grid with mesh enrichment. Tech. Rep. AIAA-94-0285 (1994)

    Google Scholar 

  36. Wendland, H.: Konstruktion und untersuchung radialer basisfunktionen mit kompaktem träger. Tech. rep. (1996)

    Google Scholar 

  37. Yates jr., E.C.: AGARD standard aeroelastic configurations for dynamic response. candidate configuration I.-Wing 445.6. Tech. Rep. Technical Memorandum 100492 (1987)

    Google Scholar 

  38. Zeng, D., Ethier, C.R.: A semi-torsional spring analogy model for updating unstructured meshes in 3D moving domains. Finite Elements in Analysis and Design 41, 1118–11,139 (2005)

    Article  Google Scholar 

  39. van Zuijlen, A.H.: Fluid-structure interaction simulations – efficient higher order time integration of partitioned systems. Ph.D. thesis, Delft University of Technology (2006)

    Google Scholar 

  40. van Zuijlen, A.H., Bijl, H.: A higher-order time integration algorithm for the simulation of non-linear fluid-structure interaction on moving meshes. Nonlinear Analysis-Theory Methods & Applications 63, 1597–1605 (2005)

    Article  Google Scholar 

  41. van Zuijlen, A.H., Bijl, H.: Implicit and explicit higher order time integration schemes for structural dynamics and fluid-structure interaction computations. Computers and Structures 83, 93–105 (2005)

    Article  Google Scholar 

  42. van Zuijlen, A.H., Bijl, H.: Implicit and explicit higher-order time integration schemes for fluid-structure interaction computations. International Journal of Multiscale Computational Engineering 4(2), 255–263 (2006)

    Article  Google Scholar 

  43. van Zuijlen, A.H., de Boer, A., Bijl, H.: Higher-order time integration through smooth mesh deformation for 3D fluid-structure interaction simulations. Journal of Computational Physics 224, 414–430 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  44. van Zuijlen, A.H., Bosscher, S., Bijl, H.: Two level algorithms for partitioned fluid-structure interaction computations. Computer Methods in Applied Mechanics and Engineering 196(8), 1458–1470 (2006)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Deltares, 177, 2600 MH, Delft, The Netherlands

    A. de Boer

  2. Delft University of Technology, 5058, 2600 GB, Delft, The Netherlands

    A. H. van Zuijlen & H. Bijl

Authors
  1. A. de Boer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. H. van Zuijlen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Bijl
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. de Boer .

Editor information

Editors and Affiliations

  1. Scientific Computing &, Centrum Wiskunde & Informatica, Science Park 123, Amsterdam, 1098 XG, Netherlands

    Barry Koren

  2. Inst. Applied Mathematics, Delft University of Technology, Mekelweg 4, Delft, 2628 CD, Netherlands

    Kees Vuik

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

de Boer, A., van Zuijlen, A.H., Bijl, H. (2009). Radial Basis Functions for Interface Interpolation and Mesh Deformation. In: Koren, B., Vuik, K. (eds) Advanced Computational Methods in Science and Engineering. Lecture Notes in Computational Science and Engineering, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03344-5_6

Download citation

Publish with us

Policies and ethics

Search

Navigation