A fundamental solution method for viscous flow problems with obstacles in a periodic array

  • Authors:

  • Hidenori Ogata;Kaname Amano;Masaaki Sugihara;Dai Okano

  • Affiliations:

  • Department of Computer Science, Faculty of Engineering, Ehime University, Matsuyama 790-8577, Japan;Department of Computer Science, Faculty of Engineering, Ehime University, Matsuyama 790-8577, Japan;Department of Computational Science and Engineering, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan;Department of Computer Science, Faculty of Engineering, Ehime University, Matsuyama 790-8577, Japan

  • Venue:
  • Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
  • Year:
  • 2003

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Abstract

We present here a fundamental solution method for two-dimensional viscous flow problems with obstacles in a two-dimensional periodic array. Our problem is mathematically a boundary value problem of the Stokes equations with periodic boundary conditions, to which it is difficult to give a good approximation by the ordinary fundamental solution method. We propose a fundamental solution method for our problem based on the periodic fundamental solution obtained by Hasimoto (J. Fluid Mech. 5 (1959) 317). In our method, the solution is approximated by using a linear combination of the periodic fundamental solutions.