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An experimental research on the flow field of water entry by pressure measurements
The underwater acoustic field in water entry of a 352 m/s blunt body has been investigated by pressure measurements. The experimental results show that from the initial stage to the later stage of wat...

Many-body effects and matrix inversion in low-Reynolds-number hydrodynamics

Phys. Fluids 13, 350 (2001); doi:10.1063/1.1331320

Issue Date: January 2001

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Kengo Ichiki
Graduate School of Human and Environmental Studies, Kyoto University, Kyoto 606-8501, Japan

John F. Brady
Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125
It is shown that the method of reflections in resistance form (with truncated multipoles) is one of many possible iterative methods to obtain the inverse of the mobility matrix (with the same truncation) in low-Reynolds-number hydrodynamics. Although the method of reflections in the mobility form is guaranteed to converge, it is found that in the resistance form the method may fail to converge. This breakdown is overcome by conjugate-gradient-type iterative methods, and the implications of the iterative method for low-Reynolds-number hydrodynamics are discussed. ©2001 American Institute of Physics.
History: Received 5 August 1999; accepted 3 October 2000
Permalink: http://link.aip.org/link/?PHFLE6/13/350/1
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KEYWORDS and PACS

Keywords
PACS
  • 47.11.+j
    Fluid dynamics Computational methods in fluid dynamics
  • 02.60.-x
    Mathematical methods in physics Numerical approximation and analysis
  • 02.10.Yn
    Mathematical methods in physics Logic, set theory, and algebra Matrix theory
  • YEAR: 2001

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PUBLICATION DATA

ISSN:
1070-6631 (print)   1089-7666 (online)
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REFERENCES (11)
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  1. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Martunus Nihhoff, Dordrecht, 1973).
  2. S. Kim and S. J. Karrila, Microhydrodynamics (Butterworth-Heinemann, Boston, 1991).
  3. L. Durlofsky, J. F. Brady, and G. Bossis, "Dynamic simulation of hydrodynamically interacting particles," J. Fluid Mech. 180, 21 (1987).
  4. J. H. C. Luke, "Convergence of a multiple reflection method for calculating Stokes flow in a suspension," SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 49, 1635 (1989).
  5. K. Ichiki, "Improvement of the Stokesian Dynamics method for systems with a finite number of particles," J. Fluid Mech. (submitted).
  6. J. F. Brady and G. Bossis, "Stokesian Dynamics," Annu. Rev. Fluid Mech. 20, 111 (1988).
  7. C. G. Jacobi, Astron. Nachr. 22, 297 (1845).
  8. R. Weiss, Parameter-Free Iterative Linear Solvers (Akademie Verlag, Berlin, 1996).
  9. S. Kim, "Stokes flow past three spheres: An analytic solution," Phys. Fluids 30, 2309 (1987).
  10. Y. Saad and M. H. Schultz, "GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems," SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 7, 856 (1986).
  11. H. A. van der Vorst, "BI-CGSTAB: A fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems," SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 13, 631 (1992).

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