A time-dependent radiation condition for transient wave-structure interactions

Abstract An extrapolated version of a time-dependent nonreflecting boundary condition is developed for use at artificial boundaries to truncate infinite/semi-infinite domains for transient water wave problems. Test examples include single- and multiple-frequency flap wavemaker problems and free vibrations of a floating circular cylinder. The finite element results compare favorably to analytical solutions. It is shown that with the proposed boundary condition the numerical simulations have little reflections from the artificial boundaries.

[1]  Chiang C. Mei,et al.  A hybrid element method for diffraction of water waves by three‐dimensional bodies , 1978 .

[2]  F. Ursell,et al.  The decay of the free motion of a floating body , 1964, Journal of Fluid Mechanics.

[3]  H. Saunders,et al.  Finite element procedures in engineering analysis , 1982 .

[4]  O. Madsen,et al.  WAVES GENERATED BY A PISTON-TYPE WAVEMAKER , 1970 .

[5]  Kwang June Bai,et al.  The added mass of two-dimensional cylinders heaving in water of finite depth , 1977, Journal of Fluid Mechanics.

[6]  David Arthur Smith Finite element analysis of the forced oscillations of ship hull forms , 1974 .

[7]  Jaw-fang Lee Finite element analysis of wave-structure interactions in the time domain , 1986 .

[8]  Warwick D. Smith A nonreflecting plane boundary for wave propagation problems , 1974 .

[9]  O. Zienkiewicz,et al.  The coupling of the finite element method and boundary solution procedures , 1977 .

[10]  J. Lysmer,et al.  Finite Dynamic Model for Infinite Media , 1969 .

[11]  Klaus-Jürgen Bathe,et al.  On effective implicit time integration in analysis of fluid–structure problems , 1980 .

[12]  F. Ursell,et al.  The transient motion of a floating body , 1970, Journal of Fluid Mechanics.

[13]  O. C. Zienkiewicz,et al.  The sommerfeld (radiation) condition on infinite domains and its modelling in numerical procedures , 1979 .

[14]  P. Schultz,et al.  Fundamentals of geophysical data processing , 1979 .

[15]  Kendall E. Atkinson An introduction to numerical analysis , 1978 .

[16]  T. Sarpkaya,et al.  Mechanics of wave forces on offshore structures , 1981 .

[17]  R. G. Dean,et al.  Forced small-amplitude water waves: a comparison of theory and experiment , 1960, Journal of Fluid Mechanics.

[18]  O. C. Zienkiewicz,et al.  Infinite elements in the study of fluid-structure interaction ppoelems , 1976 .

[19]  Richard H. Gallagher,et al.  Finite elements in fluids , 1975 .

[20]  Min-chih Huang Finite element analysis of wave interference effects between large structures , 1982 .

[21]  Peter Bettess,et al.  More on infinite elements , 1980 .

[22]  E. H. Kennard,et al.  Generation of surface waves by a moving partition , 1949 .

[23]  L. Collatz The numerical treatment of differential equations , 1961 .

[24]  B. Finlayson The method of weighted residuals and variational principles : with application in fluid mechanics, heat and mass transfer , 1972 .

[25]  Robert A. Pearson,et al.  Consistent Boundary Conditions for Numerical Models of Systems that Admit Dispersive Waves , 1974 .

[26]  I. Orlanski A Simple Boundary Condition for Unbounded Hyperbolic Flows , 1976 .

[27]  C. J. Garrison On the interaction of an infinite shallow draft cylinder oscillating at the free surface with a train of oblique waves , 1969, Journal of Fluid Mechanics.

[28]  O. C. Zienkiewicz,et al.  Diffraction and refraction of surface waves using finite and infinite elements , 1977 .

[29]  F. Ursell,et al.  ON THE HEAVING MOTION OF A CIRCULAR CYLINDER ON THE SURFACE OF A FLUID , 1949 .

[30]  B. Irons,et al.  Techniques of Finite Elements , 1979 .

[31]  J. Z. Zhu,et al.  The finite element method , 1977 .

[32]  Kwang June Bai,et al.  Diffraction of oblique waves by an infinite cylinder , 1975, Journal of Fluid Mechanics.