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RBF Morph

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RBF Morph[1][2] is a mesh morphing tool based on radial basis functions (RBFs)][3][4][5]. The morphing problem is posed defining a set of centres in the three dimensional space; for each center the three components of the displacement are prescribed. After fitting RBF field for each direction (handled as a separate scalar function) a vector valued interpolation function that allows to calculate the displacement for any given point is obtained. The same RBF smoothing function is used to move the calculation mesh related to the fluid domain acting on nodal positions. The meshless nature of the method makes straightforward its parallel use (a parallel CFD calculation is usually performed partitioning the original mesh in smaller subdomains) and its application for any kind of cell used for fluid domain discretisation (tetrahedral, hexahedral, polyhedral, prismatic, hexcore, non-conformal interfaces, etc.). A single solution can be amplified by a scalar multiplier in a non linear fashion that allows rotations to be properly accounted for; several solutions can be combined together summing their effects considering the original shape as the starting point. The result is a shape parametrization of the fluid domain. The current implementation of RBF Morph is available for the CFD solver ANSYS Fluent[6]. The user interacts with the CFD model using a GUI that allows to place centres in the domain prescribing for each one the desired displacement. RBF Morph has been awarded for the Most Advanced Approach using integrated and combined simulation methods at the European Automotive Simulation Conference (EASC). RBF Morph has been succesfully coupled with the multi-objective optimization and design environment ModeFRONTIER[7].


  1. M.E. Biancolini; C. Biancolini; E. Costa; D. Gattamelata; P.P. Valentini, Industrial Application of the Meshless Morpher RBF Morph to a Motorbike Windshield Optimisation, [European Automotive Simulation Conference (EASC)], 6-7 July 2009, Munich, Germany.
  2. M.E. Biancolini, RBF Morph: a fast meshless morpher for Fluent, presented at the EnginSoft International Conference 1-2 October 2009, Bergamo
  3. Jakobsson, S.; Amoignon, O., Mesh deformation using radial basis functions for gradientbased aerodynamic shape optimization, Computers and Fluids Volume: 36, Issue: 6, July, 2007, pp. 1119-1136.
  4. de Boer, A.; van der Schoot, M.S.; Bijl, H., Mesh deformation based on radial basis function interpolation, Computers and Structures Volume: 85, Issue: 11-14, June - July, 2007, pp. 784-795.
  5. Lodha S.K. and Franke R., Scattered Data Interpolation: Radial Basis and Other Methods, Handbook of Computer Aided Geometric Design, G. Farin, J. Hoschek and M.-S. Kim eds., North Holland, 2002.
  6. RBF Morph is an Official Partner of ANSYS Inc.[RBF Morph Page in the ANSYS Partnership Portal]
  7. M.E. Biancolini, V. Marini, Shape optimisation tools for CFD analysis: RBF Morph, Ansys Fluent and modeFRONTIER, presented as poster at EnginSoft International Conference 2009 and available online at Tor Vergata Karting Portal

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