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TECHNICAL PAPERS

Boundary Element Grid Optimization for Stokes Flow With Corner Singularities

[+] Author and Article Information
C. Pozrikidis

Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093-0411e-mail: cpozrikidis@ucsd.edu

J. Fluids Eng 124(1), 22-28 (Nov 13, 2001) (7 pages) doi:10.1115/1.1436091 History: Received May 08, 2001; Revised November 13, 2001
Copyright © 2002 by ASME
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References

Kelmanson,  M. A., 1983, “Modified Integral Equation Solution of Viscous Flows Near Sharp Corners,” Comput. Fluids, 11, No. 4, pp. 307–324.
Kelmanson,  M. A., 1983, “An Integral Equation Method for the Solution of Singular Stokes Flow Problems,” J. Comput. Phys., 51, pp. 139–158.
Hansen,  E. B., and Kelmanson,  M. A., 1994, “An Integral Equation Justification of the Boundary Conditions of the Driven-Cavity Problem,” Comput. Fluids, 23, No. 1, pp. 225–240.
Kelmanson,  M. A., and Longsdale,  B., 1995, “Annihilation of Boundary Singularities Via Suitable Green’s Functions,” Comput. Math. Appl., 29, No. 4, pp. 1–7.
Ingber,  M. S., and Mitra,  A. K., 1986, “Grid Optimization for the Boundary Element Method,” Int. J. Numer. Methods Fluids, 23, pp. 2121–2136.
Mackerle,  J., 1993, “Mesh Generation and Refinement for FEM and BEM—A Bibliography (1990–1993),” Finite Elem. Anal. Design, 15, pp. 177–188.
Liapis,  S., 1994, “A Review of Error Estimation and Adaptivity in the Boundary-Element Method,” Eng. Anal. Boundary Elem., 14, No. 4, pp. 315–323.
Abe,  K., and Sakuraba,  S., 1999, “An HR-Adaptive Boundary Element for Water Free-Surface Problems,” Eng. Anal. Boundary Elem., 23, pp. 223–232.
Muci-Küchler,  K. H., and Miranda-Valenzuela,  J. C., 2001, “Guest Editorial,” Eng. Anal. Boundary Elem., 25, pp. 477–487.
Dean,  W. R., and Montagnon,  P. E., 1949, “On the Steady Motion of Viscous Liquid in a Corner,” Proc. Cambridge Philos. Soc., 45, pp. 389–394.
Moffatt,  H. K., 1964, “Viscous and Resistive Eddies Near a Sharp Corner,” J. Fluid Mech., 18, pp. 1–18.
Pozrikidis, C., 1997, Introduction to Theoretical and Computational Fluid Dynamics Flow, Cambridge University Press.
Pozrikidis, C., 1992, Boundary Integral and Singularity Methods for Linearized Viscous Flow, Cambridge University Press.
Pozrikidis,  C., 1999, “A Spectral-Element Method for Particulate Stokes Flow,” J. Comput. Phys., 156, pp. 360–381.
Pozrikidis,  C., 2001, “Dynamical Simulation of the Shear Flow of Suspensions of Particles with Arbitrary Shapes,” Eng. Anal. Boundary Elem., 25, pp. 19–30.
Wannier,  G. H., 1950, “A Contribution to the Hydrodynamics of Lubrication,” Q. Appl. Math., 8, No. 1, pp. 1–32.

Figures

Grahic Jump Location
Illustration of two-dimensional Stokes flow past a stationary body located above an infinite plane wall
Grahic Jump Location
Streamline pattern of (a) antisymmetric and (b) symmetric flow around a corner with aperture angle 2α=3π/2. (c) Branches of the real and imaginary part of λ for antisymmetric flow (thick lines) and symmetric flow (thin lines); the solid lines represent the real part, and the dashed lines represent the imaginary part.
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Force and torque exerted on a square cylinder with side length a whose center is located at distance a above the plane wall, plotted against the element stretch ratio β for Ns=8, 16, 32, and 64 boundary elements along each side. The highest curve in (a) and the lowest curve in (b) correspond to Ns=64.
Grahic Jump Location
Streamline pattern of shear flow past a square computed with the nearly optimal element distribution of 16 elements along each side, for inclination angle (a) 0, (b) π/4, and (c) π/2. (d) Flow past an inclined square whose center is located at a distance equal to five times the side length above the wall. The dots mark the location of the boundary element nodes.
Grahic Jump Location
Contribution of the top elements to the line integral of the traction defining the force corresponding to Fig. 4(a)
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Distribution of the shear stress along the upper side of the square illustrated in Fig. 4(a), plotted against the arc length measured from the northwestern corner
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Distribution of shear stress with respect to arc length measured from the left and top corners for the flow illustrated in Fig. 4(d)
Grahic Jump Location
Streamline patterns of simple shear flow past a surface-mounted square and section of a circular cylinder

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