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Validation of a Galerkin technique on a boundary integral equation for creeping flow around a torus

Abstract

A validation of the numerical solution for the steady and axisymmetric creeping flow around a three-dimensional torus is presented. This solution is obtained by means of the boundary element method. Both a Galerkin weighting technique and collocation to the centroid of the elements are employed. The curve of the viscous drag force as a function of the diameter of the torus relative to its thickness is compared against a semi-analytical solution and laboratory experimental measurements taken from the literature. The semi-analytical solution, as it is known for this kind of geometry, involves the Legendre functions of first and second kind of order one and semi-integer degrees, also called toroidal harmonics.

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Acknowledgments

This work has received financial support from Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET, Argentina, grant PIP 112-20111-00978), Universidad Nacional del Litoral (UNL, Argentina, Grant CAI+D 2009-III-4-2), Agencia Nacional de Promoción Científica y Tecnológica (ANPCyT, Argentina, grants PICT 2010-2492/16, PICT 2009-1141/07, PICT-PRH 2009-0147), EU-IRSES (PIRSES-GA-2009-246977), and was performed with the Free Software Foundation /GNU-Project resources such as GNU-Linux-OS, GNU-GFortran, GNU-Octave, GNU-Git, GNU-Doxygen, and GNU-GIMP, as well as other Open Source resources as NETGEN, ParaView, OpenDX, Xfig and LATEX.

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Correspondence to Jorge D’Elía.

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Communicated by Gustavo Buscaglia.

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Sarraf, S., López, E., Ríos Rodríguez, G. et al. Validation of a Galerkin technique on a boundary integral equation for creeping flow around a torus. Comp. Appl. Math. 33, 63–80 (2014). https://doi.org/10.1007/s40314-013-0043-5

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Keywords

  • Creeping flow
  • Steady flow
  • Boundary element method
  • Collocation technique
  • Galerkin weighting
  • Toroidal harmonics

Mathematics Subject Classification (2000)

  • 65N38
  • 76D07