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Direct second kind boundary integral formulation for Stokes flow problems

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Abstract

A direct boundary element method is formulated for the Stokes flow problem based on an integral equation representation for the components of traction. For problems in which the components of velocity are prescribed on the boundary of the domain, this new formulation results in a hypersingular Fredholm integral equation of the second kind. A method of regularization to evaluate the hypersingular integral is discussed. For certain problems involving flows about particles, the integral equation representation for the tractions is not unique because of the existence of rigid body eigenmodes. A method to constrain out these rigid body modes is also discussed. Several example problems are considered in which this new formulation is compared to more traditional boundary element formulations.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of New Mexico, 87131, Albuquerque, New Mexico, USA

    M. S. Ingber

  2. Fluid and Thermal Sciences Department, Sandia National Laboratories, 87185, Albuquerque, New Mexico, USA

    L. A. Mondy

Authors
  1. M. S. Ingber
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  2. L. A. Mondy
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Communicated by S. N. Atluri, July 6, 1992

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Ingber, M.S., Mondy, L.A. Direct second kind boundary integral formulation for Stokes flow problems. Computational Mechanics 11, 11–27 (1993). https://doi.org/10.1007/BF00370070

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