Radial Basis Functions for Interface Interpolation and Mesh Deformation

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.

[1]  E. Kansa.  Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—I surface approximations and partial derivative estimates , 1990 .

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

[3]  C. R. Ethier,et al.  A semi-torsional spring analogy model for updating unstructured meshes in 3D moving domains , 2005 .

[4]  John Batina,et al.  Unsteady Euler algorithm with unstructured dynamic mesh for complex-aircraft aeroelastic analysis , 1989 .

[5]  Guiyong Zhang,et al.  A residual based error estimator using radial basis functions , 2008 .

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

[7]  Charbel Farhat,et al.  A three-dimensional torsional spring analogy method for unstructured dynamic meshes , 2002 .

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

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

[10]  Charbel Farhat,et al.  On a component mode synthesis method and its application to incompatible substructures , 1994 .

[11]  Charbel Farhat,et al.  Partitioned analysis of coupled mechanical systems , 2001 .

[12]  A. Przekwas,et al.  Unsteady flow computation using moving grid with mesh enrichment , 1994 .

[13]  Alain Combescure,et al.  Multi-time-step explicit–implicit method for non-linear structural dynamics , 2001 .

[14]  Hester Bijl,et al.  Iterative solution techniques for unsteady flow computations using higher order time integration schemes , 2005 .

[15]  Hester Bijl,et al.  Implicit and Explicit Higher-Order Time Integration Schemes for Fluid-Structure Interaction Computations , 2006 .

[16]  Carlos E. S. Cesnik,et al.  EVALUATION OF SOME DATA TRANSFER ALGORITHMS FOR NONCONTIGUOUS MESHES , 2000 .

[17]  Martin W. Heinstein,et al.  A three dimensional surface‐to‐surface projection algorithm for non‐coincident domains , 2003 .

[18]  Hester Bijl,et al.  Review of coupling methods for non-matching meshes , 2007 .

[19]  Hester Bijl,et al.  Two level algorithms for partitioned fluid-structure interaction computations , 2006 .

[20]  A. H. van Zuijlen,et al.  Fluid-structure interaction simulations: Efficient higher order time integration of partitioned systems , 2006 .

[21]  Hester Bijl,et al.  A higher-order time integration algorithm for the simulation of nonlinear fluid–structure interaction , 2005 .

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

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

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

[25]  P. Tallec,et al.  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 , 1998 .

[26]  E. Carson Yates,et al.  AGARD standard aeroelastic configurations for dynamic response , 1989 .

[27]  P. Knupp.  Algebraic mesh quality metrics for unstructured initial meshes , 2003 .

[28]  E. Carson Yates,et al.  AGARD standard aeroelastic configurations for dynamic response. Candidate configuration I.-wing 445.6 , 1987 .

[29]  K. Kovalev,et al.  Unstructured Hexahedral Non-conformal Mesh Generation , 2005 .

[30]  Richard K. Beatson,et al.  Smooth surface reconstruction from noisy range data , 2003, GRAPHITE '03.

[31]  Martin D. Buhmann,et al.  Radial Basis Functions , 2021, Encyclopedia of Mathematical Geosciences.

[32]  Yucheng Liu,et al.  Optimum design of straight thin-walled box section beams for crashworthiness analysis , 2008 .

[33]  H. Bijl,et al.  Implicit and explicit higher order time integration schemes for structural dynamics and fluid-structure interaction computations , 2005 .

[34]  Carlos E. S. Cesnik,et al.  Evaluation of computational algorithms suitable for fluid-structure interactions , 2000 .

[35]  E. Kansa.  MULTIQUADRICS--A SCATTERED DATA APPROXIMATION SCHEME WITH APPLICATIONS TO COMPUTATIONAL FLUID-DYNAMICS-- II SOLUTIONS TO PARABOLIC, HYPERBOLIC AND ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS , 1990 .

[36]  M. Hafez,et al.  Computational fluid dynamics review 1995 , 1995 .

[37]  M. Unser,et al.  Interpolation revisited [medical images application] , 2000, IEEE Transactions on Medical Imaging.

[38]  J. Kok,et al.  A Simple, Robust and Fast Algorithm to Compute Deformations of Multi-Block Structured Grids , 2002 .

[39]  Hester Bijl,et al.  Implicit Time Integration Schemes for the Unsteady Compressible Navier–Stokes Equations: Laminar Flow , 2002 .

[40]  H. Wendland,et al.  A new multivariate interpolation method for large-scale spatial coupling problems in aeroelasticity , 2005 .

[41]  R. Beatson,et al.  Smooth fitting of geophysical data using continuous global surfaces , 2002 .

[42]  Guru P. Guruswamy,et al.  A Parallel Multiblock Mesh Movement Scheme For Complex Aeroelastic Applications , 2001 .

[43]  Stephen Billings,et al.  Interpolation of geophysical data using continuous global surfaces , 2002 .

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

[45]  U. Meissner,et al.  Finite elements in water resources. , 1982 .