A numerical approach to the determination of 3d stokes flow in polygonal domains using PIES

  • Authors:

  • Eugeniusz Zieniuk;Krzysztof Szerszen;Marta Kapturczak

  • Affiliations:

  • Faculty of Mathematics and Computer Science, University of Bialystok, Bialystok, Poland;Faculty of Mathematics and Computer Science, University of Bialystok, Bialystok, Poland;Faculty of Mathematics and Computer Science, University of Bialystok, Bialystok, Poland

  • Venue:
  • PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part I
  • Year:
  • 2011

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Abstract

This paper discusses a generalization of intensively developed parametric integral equation system (PIES) to solve 3D steady Stokes flow. Given the preliminary nature of this research, the effectiveness of the generalized PIES has been verified for the solutions of the Stokes problems defined on polygonal domains. The boundary of such domains has been modeled directly in PIES by joining rectangular Coons parametric patches of the first degree. With them it is possible to model relatively large linear segments of the boundary by small number of corner points of the considered polygonal domain. Two numerical examples were used to validate the solutions of PIES with analytical and numerical results available in the literature.