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Applications of Boundary Element Methods to Fluid Mechanics

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Topics in Boundary Element Research

Abstract

In this chapter we make an effort to review the applications of boundary methods to fluid mechanics. At the outset we wish to give our definition of boundary methods. First, we exclude such techniques from the general class of finite element methods. Although some of the language and a few of the numerical techniques of the two methods have merged, they are historically quite separate.

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References

  1. Trefftz, E., Über die Kontraktion kreisförmiger Flüssigkeitsstrahlen. Z. Math. Phys., 64, 34, 1917

    Google Scholar 

  2. Jaswon, M. A., Symm, G. T., Integral Equation Methods in Potential Theory and Elastostatics. Academic Press, 1977

    Google Scholar 

  3. Brebbia, C. A., The Boundary Element Method for Engineers. John Wiley and Sons, 1978

    Google Scholar 

  4. Brebbia, C. A., Walker, S., Boundary Element Techniques in Engineering. Newnes-Butterworths 1980

    Google Scholar 

  5. Banerjee, P. K, Butterfield, R., Boundary Element Methods in Engineering Science. McGraw-Hill 1981

    Google Scholar 

  6. Liggett, J. A., Liu, P. L.-F., The Boundary Integral Equation Method for Porous Media Flow. George Allen Unwin, 1983

    Google Scholar 

  7. Crouch, S. L., Starfield, A. M., Boundary Methods in Solid Mechanics. George Allen and Unwin, 1983

    Google Scholar 

  8. Mukherjee, S., Boundary element methods in creep and fracture. Applied Science Publishers, Ltd, Essex, 1982, Also Elsevier Science Publishing, Co, N.Y.

    Google Scholar 

  9. Green, G., An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism, Nottingham 1828

    Google Scholar 

  10. Hunt, B. W., Numerical solutions of an integral equation for flow from a circular orifice. Jour. Fluid Mech., 31, 361–377, 1968

    Article  MATH  Google Scholar 

  11. Prager, W., Die Druckverteilung an Körpern in ebener Potentialströmung. Physik. Zeitschr., 29, 865–869, 1928

    Google Scholar 

  12. Nyström, E. J., Über die praktische Auflösung von linearen Integralgleichungen mit Anwendungen auf Randwertaufgaben der Potentialtheorie. Soc. Sci. Fennica, Comment. Physico-Math., 415, 1–52, 1928

    Google Scholar 

  13. Fredholm, I., Sur une classe d’equations fonctionelles. Acta Math., 27, 365–390, 1903

    Article  MathSciNet  MATH  Google Scholar 

  14. Lotz, L, Calculation of potential past airship bodies in yaw. NACA TM 675, 1932 [also Ingenieur-Archiv, Vol. I I, 1931 ]

    Google Scholar 

  15. Vandrey, F., A direct iteration method for the calculation of velocity distribution of bodies of revolution and symmetrical profiles. Admiralty Research Lab. Rept. R 1/G/HY/12/2, 1951

    Google Scholar 

  16. Weinstein, A., On axially symmetric flows. Quarterly of Applied Math., 5, No. 4, 1948

    Google Scholar 

  17. Van Tuyl, A., On the axially symmetric flow around a new family of half bodies. Quarterly of Applied Math., 7, No. 4, 1950

    Google Scholar 

  18. Sadowsky, M. A., Sternberg, E., Elliptic integral representation of axially symmetric flows. Quarterly of Applied Math. 8, No. 2, 1950

    Google Scholar 

  19. Landweber, L., The axially symmetric potential flow about elongated bodies of revolution. David Taylor Model Basin Rep., 761, 1951

    Google Scholar 

  20. Vandrey, F., On the calculation of the transverse potential flow past a body of revolution with the aid of the method of Mrs. Flügge-Lotz. Astia AD-40089, 1951

    Google Scholar 

  21. Smith, A. M. O., Pierce, J., Exact solution of the Neumann problem. Calculation of plane and axially symmetric flows about or within arbitrary boundaries. Douglas Aircraft Company Report No. 26988, 1958 [Summary in Proc. of the 3rd Int. Congress of Applied Math., Brown University, 1958 ]

    Google Scholar 

  22. Hess, J. L., Smith, A. M. O., Calculation of nonlifting potential flow about arbitrary three-dimensional bodies. ES 40622, Douglas Aircraft Corp., Long Beach, Calif. 1962 (Also in Jour. of Ship Research 8, No. 2, Sept. 1964 )

    Google Scholar 

  23. Davenport, F. J., Singularity solutions to general potential flow airfoil problem. D6–7207, Boeing Airplane Co., Seattle, Wash. 1963

    Google Scholar 

  24. Jaswon, M. A., Integral equation methods in potential theory: I. Proc. Royal Soc. A, 275, 23–32, 1963

    MathSciNet  MATH  Google Scholar 

  25. Symm, G. T., Integral equation methods in potential theory; II. Proc. Royal Soc. A, 275, 33–46, 1963

    MathSciNet  MATH  Google Scholar 

  26. Chaplin, H. R., A method for numerical calculation of slip stream contraction of a shrouded impulse disk in the static case with application to other axisymmetric potential flow problems. David Taylor Model Basin Report No. 1857, 1964

    Google Scholar 

  27. Gallagher, R. H., Finite Element Analysis Fundamentals, Prentice Hall 1975

    Google Scholar 

  28. Hess, J. L., Review of integral-equation techniques for solving potential-flow problems with complicated boundaries. Innovative Numerical Analysis for the Applied Engineering Sciences. University Press of Virginia, Charlottesville, 131–143, 1980

    Google Scholar 

  29. Hunt, B., The mathematical basis and numerical principles of the boundary integral equation method for incompressible potential flow over 3-D aerodynamic configurations. In: Numerical Methods in Applied Fluid Dynamics (B. Hunt, ed.), Academic Press, 49–135, 1980

    Google Scholar 

  30. Carey, G. F., Extension of boundary elements to lifting compressible aerodynamics. In: Finite Element Flow Analysis (T. Kawai, ed.), Univ. of Tokyo Press, 939–943, 1982

    Google Scholar 

  31. Carey, G. F., Kim, S. W., Extension of boundary element method to lifting subcritical flows. 19th Annual Meeting, Society of Engineering Science, University of Missouri-Rolla, 1982

    Google Scholar 

  32. Inamuro, T., Adachi, T., Sakata, H., A numerical analysis of unsteady separated flow by discrete vortex model using boundary element method. In: Finite Element Flow Analysis (T. Kawai, ed.), University of Tokyo Press, 931–938, 1982

    Google Scholar 

  33. White, J. W., Kline, S. J., A calculation method for incompressible axisymmetric flows, including unseparated, fully separated, and free surface flows. Report MD-35, U.S. Air Force Office of Scientific Research Mechanics Divison, Contract AF-F44620–74-C-0016; Thermosciences Division, Department of Mechanical Engineering, Stanford University, 1975

    Google Scholar 

  34. Wu, J. C., Problems of general visous flow. In: Developments in Boundary Element Methods — 2 (P. K. Banerjee and R. P. Shaw, eds.). Applied Science Publishers, 69–109, 1982

    Google Scholar 

  35. Wu, J. C., Thompson, J. F., Numerical solutions of time-dependent incompressible Navier-Stokes equations using an integro-differential formulation. Computers and Fluids 1, 197–215, 1973

    Article  MATH  Google Scholar 

  36. Lennon, G. P., Liu, P. L-F., Liggett, J. A., Boundary integral equation solution to axisymmetric potential flows, 1, Basic formulation. Water Resources Research, 15 (5), 1102–1106, 1979

    Article  Google Scholar 

  37. Lennon, G. P., Liu, P. L-F., Liggett, J. A., Boundary integral equation solution to axisymmetric flows, 2, Recharge and well problems in porous media. Water Resources Research, 15 (5), 1107–1115, 1979

    Article  Google Scholar 

  38. Lennon, G. P., Liu, P. L-F., Liggett, J. A., Boundary integral solutions to three-dimensional unconfined Darcy’s flow. Water Resources Research, 16 (4), 651–658, 1980

    Article  Google Scholar 

  39. Cheng, A H-D., Liu, P. L-F., Liggett, J. A., Boundary calculations of sluice and spillway flows. J. of the Hydraulics Division, ASCE, 107, (10), 1163–1178, 1981

    Google Scholar 

  40. Liggett, J. A, Salmon, J. R., Cubic spline boundary elements. Int. J. for Numerical Methods in Engineering, 17, 543–556, 1981

    Article  MATH  Google Scholar 

  41. Liu, P. L-F., Liggett, J. A., Applications of boundary element methods to problems of water waves. In: Developments in Boundary Element Methods - 2 (P. K. Banerjee and R. P. Shaw, eds.), Elsevier’s Applied Science Publishers, Ltd., 37–67, 1982

    Google Scholar 

  42. Nakayama, T., Washizu, K., The boundary element method applied to the analysis of two-dimensional nonlinear sloshing problems. Int. J. Num. Meth. Engrg., 17, No. 11, 1631–1646, 1981

    Article  MATH  Google Scholar 

  43. Washizu, K., Some applications of finite element techniques to nonlinear free surface fluid flow problems. In: Finite Element Flow Analysis (T. Kawai, ed.). Univ. of Tokyo Press, 3–15, 1982

    Google Scholar 

  44. Faltinsen, O. M., A numerical nonlinear method of sloshing in tanks with two-dimensional flow. J. Ship Research, 23 (3), 193–202, 1978

    Google Scholar 

  45. Longuet-Higgins, M. S., Cokelet, E. D., The deformation of steep surface waves on water. I. A numerical method of computation. Proc. of the Royal Society, A 350, 1–25, 1976

    MathSciNet  MATH  Google Scholar 

  46. Cokelet, E. D., Breaking waves - the plunging jet and interior flow-field. Proc. Sym. on Mechanics of Wave-induced Forces on Cylinders, Bristol, 1978

    Google Scholar 

  47. Vinje, T., Brevig, P., Numerical solution of breaking waves. Adv. Water Resources, 4, 77–82, 1981

    Article  Google Scholar 

  48. Vinje, T., Brevig, P., Numerical calculations of forces from breaking waves. Preprints, Int. Sym. on Hydrodynamics in Ocean Engineering, Trondheim, Norway, 547–566, 1981

    Google Scholar 

  49. Issacson, M. de St. Q., Nonlinear-wave effects on fixed and floating bodies. J. Fluid Mechanics, 120, 267–281, 1982

    Article  Google Scholar 

  50. Engquist, B., Majda, A., Absorbing boundary conditions for the numerical simulation of waves. Math. and Computers, 31, 629–651, 1977

    Article  MathSciNet  MATH  Google Scholar 

  51. Smith, W. D., A non-reflecting boundary for wave propagation problems. J. Computational Physics, 15, 492–503, 1974

    Article  MATH  Google Scholar 

  52. Betts, P. L., Mohamad, T. T., Water waves: A time-varying unlinearized boundary element approach. Finite Element Flow Analysis (T. Kawai, ed.), University of Tokyo Press, 923–929, 1982

    Google Scholar 

  53. LeMéhauté, B., Progressive wave absorber. J. Hyd. Res., 10 (2), 153–169, 1972

    Article  Google Scholar 

  54. Salmon, J. R., Liu, P. L-F., Liggett, J. A., Integral equation method for linear water waves. J. Hydraulics Division, ASCE, 106, (12), 1995–2010, 1980

    Google Scholar 

  55. Lennon, G. P., Liu, P. L-F., Liggett, J. A., Boundary integral solutions of water wave problems. J. Hydraulics Division, ASCE, 108 (8), 921–931, 1982

    Google Scholar 

  56. Mills, R. D., Computing internal viscous flow problems for the circle by integral methods. J. Fluid Mech., 79 (3), 609–624, 1977

    Article  MATH  Google Scholar 

  57. Okabe, M., A boundary element approach in the incompressible viscous flow. In: Finite Element Flow Analysis (T. Kawai, ed.). Univ. of Tokyo Press, 915–922, 1982

    Google Scholar 

  58. Biot, M. A., General theory of three-dimensional consolidation. J. of Applied Physics, 12, 155–164, 1941

    Article  MATH  Google Scholar 

  59. Biot, M. A., Theory of elasticity and consolidation for a porous anisotropic solid. J. of Applied Physics, 26, 182–185, 1955

    Article  MathSciNet  MATH  Google Scholar 

  60. Cleary, M. P., Fundamental solutions for a fluid-saturated porous solid. Int. J. of Solids and Structures, 13, 785–806, 1977

    Article  MathSciNet  MATH  Google Scholar 

  61. Cleary, M. P., Moving singularities in elasto-diffusive solids with applications to fracture propagation. Int. J. of Solids and Structures, 14, 81–97, 1978

    Article  MATH  Google Scholar 

  62. Cleary, M. P., Fundamental solutions for fluid-saturated porous media and applications to local rupture phenomena. Thesis submitted in partial fulfillment of requirements for for the Ph.D. degree, Brown University, 1976

    Google Scholar 

  63. Cheng, A H-D., Liggett, J. A., Boundary integral equation method for linear porous-elasticity with applications to fracture propagation. Int. J. for Numerical Methods in Engineering, (In press), 1983

    Google Scholar 

  64. Cheng, A H-D., Liggett, J. A, Boundary integral equation method for linear porous-consolidation. Int. J. for Numerical Methods in Engineering, (In press), 1983

    Google Scholar 

  65. Liggett, J. A, Hydrodynamic calculations using boundary elements. In: Finite Element Flow Analysis (T. Kawai, ed.), Univ. of Tokyo Press, 889–896, 1982

    Google Scholar 

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Authors
  1. J. A. Liggett
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  2. P. L.-F. Liu
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Editor information

Editors and Affiliations

  1. Department of Civil Engineering, The University, SO9 5NH, Southampton, England

    Carlos A. Brebbia

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© 1984 Springer-Verlag Berlin Heidelberg

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Liggett, J.A., Liu, P.LF. (1984). Applications of Boundary Element Methods to Fluid Mechanics. In: Brebbia, C.A. (eds) Topics in Boundary Element Research. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2877-1_5

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  • DOI: https://doi.org/10.1007/978-1-4899-2877-1_5

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-387-13097-2

  • Online ISBN: 978-1-4899-2877-1

  • eBook Packages: Springer Book Archive

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