ࡱ> jli)` Rbjbj2Tlllllll|,M+ r)t)t)t)t)t)t)$e/h1:)Yl!!!)ll* R)R)R)!Vllr)R)!r)R)R)llR) V2Q&nR)r)+<M+R)2H)3R)22$lR) |lR)2l))H) M+!!!!$ $ llllll oNN~NoQ[ 1 Analytical representations of linear free-surface potential flows bJTN{NH\lxvzXT 1983t^nNS'Yf[4l)R] zf[Xf[MO 1988t^lVWSyr'Yf[4lRRf[ZS Xf[MO sNlV9~>yxvz4lRRR;NNTVExST\O;NN0 Q[With the presence of a free surface, potential flows of fluid underneath are commonly described by an integral representation resultant from the application of Fourier transformation. In the three-dimensional water wave problems, the double Fourier integral with respect to the wavenumber vectors associated with the horizontal space coordinates is derived to represent flow characteristics such as flow velocity, pressure, velocity potential and free-surface wave profile. The double Fourier integral can represent a potential flow due to any distribution of singularities corresponding to a source, a line, a surface or a complete hull with a pulsating density or/and advancing in fluid. Without loss of generality, we analyze the potential flow due to a source; commonly called the Green function including the cases of zero-speed, steady flow and more general of unsteady flows with forward speed. Unlike the traditional ways to treat first the k-integral in the double Fourier integral in (k, q) plane, we evaluate first the q-integral by using the Cauchy theorem of residues. A single k-integral is then obtained to represent the potential flow. The analyses on the single k-integral give some new insights to characteristic behaviors of water waves on the free surface. This analytical representation is critically important when we evaluate a potential flow due to an arbitrary distribution of singularities instead of a source, in which case the involved spectrum function is usually given by an expression analytically (easy to integrate) in q but complicated (difficult to integrate analytically) in k. This new development provides a breakthrough and efficient way to evaluate the potential flows in the complex free surface problems. 2 Uniform asymptotic expansion of Interfacial Viscous Ship Waves bJTN{N4ba_ T\n]N'Yf[Zwm 96] zf[boRYec xvzeT:N96Nwm m] z4lRR f[S|l|~T:_^!h8h0 Q[The interfacial waves due to a steady Oseenlet in a system of two semi-infinite immiscible fluids of different densities are investigated by Lu and Chwang (2005). The two-fluid system which consists of an upper inviscid and a lower viscous fluid is assumed to be incompressible, homogenous and stable. The interfacial elevation is given by a double Fourier integral, which involves a generic amplitude function, a complex dispersion function and an elementary phase function. The saddle points are those at which the gradient of the phase function vanishes. There are two real saddle points for  EMBED Equation.3 , where  EMBED Equation.DSMT4  is along the azimuth angle and  EMBED Equation.DSMT4 = 0 is the moving path of the poinf force. The two saddle points are complex and conjugate for  EMBED Equation.DSMT4 . These points coalesce at  EMBED Equation.DSMT4  when  EMBED Equation.DSMT4 . The asymptotic behaviour of the far-field wave profiles depends on the contribution from the two real saddle points within the Kelvin wedge  EMBED Equation.DSMT4  and one complex saddle point in the outer region  EMBED Equation.DSMT4  respectively. Both approximations fail around the cusp lines  EMBED Equation.DSMT4  which correspond to a coalescent pair of saddle points in the Fourier integrals. The third approximation using Airy functions which is valid locally for  EMBED Equation.DSMT4  can be derived. These local approximations are limited in their domains of validity, and can not always be matched up. These have been shown by Lu and Chwang (2007). After the use of the CFU method ( Chester, Friedman ,Ursell, 1957) in the  HYPERLINK "http://www.iwwwfb.org/Abstracts/iwwwfb28/iwwwfb28_15.pdf" evaluation of time-domain capillary-gravity Green function, we continue to extend its application to analyse the behaviour of the interfacial viscous waves in far field. A cubic transform of the variable of integration is introduced and uniformly valid asymptotic expansions in terms of the Airy functions and its derivatives are presented which span three separate domains for  EMBED Equation.DSMT4  greater than, near , and less than EMBED Equation.DSMT4 . Using appropriate expansions for the Airy function , the new results is consistent with simpler approximations which apply away from  EMBED Equation.DSMT4 , based on the method of stationary phase. Calculations are performed to illustrate the utility of the asymptotic results. 3 TEBEM and High-order derivatives of the GF bJTN{Nke mYec T\n] z'Yf[ZSXu[^ Ye萌TV[YN@\ 111R mwm] zyf[Nb/gRe_zfW0W#N,|QN-NV 9] zf[O96Rf[f[/gYXTOoR;NN -NV 9] zf[O}wNT^f[~oR~ ]NTOo`S96)n[lSOc>e]\O~N[ VE9!jՋ4l`l'YOITTC ljm-N3z'`N[YXTOYXTV2y]@\W@xyxĉR^(uRf[N[~N[ 096Rf[ 00 04lRRf[xvzNۏU\ 00 0Journal of Marine Science and Application 00 0-NV09xvz 0I{g RYVv[ 9f[ORINA OXT0 Q[ We will discuss the Taylor Expansion Boundary Element(TEBEM) method and some new results. Focus will play on the property of the high-order derivatives(second order) of the integration of normal dipole on the element and its property. 4 Green function with viscosity and surface tension effects for a three -dimensional Kelvin source bJTN{N1)h 'Yޏt]'Yf[ZSXu f'Yޏt]'Yf[f[/gef0 pgQxvzuyS. 2)[zfYec 'Yޏt]'Yf[96] zf[bZSXu[^ |QNV2~0VE{Rf[f[ObXT0]NňY~gRgV[͑p[[f[/gYXTObXT096Nwm m] zw͑p[[;NN096Ջ4l`l;NNfNeRaWؚ'`{xvzbؚ~] z^0;`] z^ eRaWV[yb@\ZSXu[^fcVEy\Ng0W] zOSISOPE gsOeVY  0A study of crack monitoring of ship structures 0. Q[This paper investigates the properties of the free-surface Green function for a three-dimensional Kelvin source taking the viscosity and surface tension effects into consideration. This free-surface Green function is of practical importance to the analyses of hydrodynamic loads exerting on a floating body or a fully submerged object operating steadily in the calm water with infinite water depth. Based on the linearized free-surface boundary condition considering the viscosity and surface tension, the free-surface Green function for a three-dimensional steady transient source in an analytical form is first derived. Then, an efficient and accurate technique is described for computing both local and wave components of the free-surface Green function with viscosity and surface tension effects. It is shown that not only can the combine effects of viscosity and surface tension eliminate the non-physical short waves, but also solve singular properties of the Green function. 5 Flexural-gravity wave resistances due to a line source steadily moving on a floating thin elastic plate bJTN{NbSN:_Yec Nwm'Yf[ZSXu[^ N 0Theoretical and Applied Mechanics Letters 0 YXTOYXT0 04lRRf[xvzNۏU\ 0YXTOYXT0 0Journal of Hydrodynamics 0gbLYXTOyfN|QYXT0 0Journal of Shanghai University (English Edition) 0YXTOYXT0 0IAENG International Journal of Applied Mathematics 0YXTOYXT0-NVRf[f[OAmSORf[NNYXTO4lRRf[NN~~XT0xvzcYyDR0 Q[ Analytical solutions for the flexural-gravity wave resistances due to a line source steadily moving on the surface of an infinitely deep fluid are investigated within the framework the linear potential theory. The homogenous fluid, covered by a thin elastic plate, is assumed to be incompressible and inviscid, and the motion to be irrotational. The line source is represented by the Dirac delta function, which can be seen as the fundamental singularity for a continuously distributed load. The solution in integral form for the wave resistance is obtained by means of the Fourier transform and the explicitly analytical solutions are derived with the aid of the residue theorem. The dispersion relation shows that there is a minimal phase speed, a threshold for the existence of the wave resistance. No wave is generated when the moving speed of the source is less than the minimal phase speed. When the moving speed is greater than the minimal phase speed, the flexural and gravity waves propagate in the leading and trailing regions of the moving load, respectively, and the wave resistances first increase to their peak values and then decrease. The effects of the flexural rigidity and the inertia of the plate are studied. 6 MultiSmart3D --- A special Green s function software product for efficient and accurate applications in layered pavements bJTN{NErnian Pan received his BS and MS degrees from China (Lanzhou University and Beijing University) and his PhD from University of Colorado at Boulder. He joined the University of Akron in 2002 and was promoted to full professor in 2008, with a primary appointment in the Department of Civil Engineering. Ernians teaching and research are in continuum/computational mechanics and structure mechanics using the Greens function method. His Greens function solutions are also applied to earth science and modern engineering problems including earth/pavement deformation due to surface and internal loadings, mechanical and electronic properties of nanoscale quantum heterostructures, and mangetoelectric effect in multiferroic composites. He has published over 230 peer-reviewed journal articles and is a reviewer for many different journals. He is a fellow of ASCE and ASME and associate editor of Mechanics Research Communications. As his research/teaching is multidisciplinary, he is always looking for experts from different fields to collaborate with and to learn from. Q[ : Layered flexible pavements pose great challenges to pavement engineers as well as to mathematicians. In this talk, I will present our newly developed Green s function-based forward program MultiSmart3D. This program is based on the novel cylindrical system of vector functions combined with the propagator matrix method. In our calculation, any number of observation points can be assigned to the layered pavement in any location and the pavement can be basically made of any number of layers (while the existing programs are all limited to 26 output points and 20 sublayers/layers). In the applications, the temperature-dependent modulus variation with depth is used as input, which requires that the pavement is subdivided into many sublayers (over 500). We showed that the pavement responses based on the real modulus variation with depth and those based on the averaged moduli can be substantial. Consequently, the corresponding fatigue and rutting lives based on these two pavement profiles are remarkably different. General normal loading and shearing over the surface of transversely isotropic layered half space are also discussed, including their influence on the pavement safety. 7 Numerical Integration of Singular Kernels of Green Function and Its Derivatives bJTN{NBin TENG, Received his Ph. D. from Dalian University of Technology, China, 1989. From Dec., 1990 to Jan., 1993 worked in Department of Engineering Science, University of Oxford, United Kingdom as a Post-doctoral Research Assistant to Prof. Eatock Taylor. From Feb., 1993 to Feb. 1995 was an Associate Professor at Department of Civil Engineering, Dalian University of Technology, China. From Aug., 1996 to Present, a Professor at Department of Civil Engineering, Dalian University of Technology, China. In Sept., 2001 to Sept. 2006, was appointed as a Cheung Scholar under Cheung Kong Award Program by Education Ministry of China. Q[Green s function is widely used in the computation of water wave problem with the boundary element method. However, when a field point is close to the source point, Green s function and its derivative approach infinity with a speed of 1/r and 1/r2 for three dimensional problems. Wherefore, the integration in an element which includes or is near to the source point is a singular integration, which exists only at Cauchy principle sense or a near singular integration. In the present presentation, some direct integration methods are introduced for computing the free term coefficient, the Cauchy principal value integral and near-singular integration in the high order boundary element method. Numerical experiments are carried out to examine the computation accuracy and convergence speed of the method for the free term coefficient and Cauchy principal value integration. The numerical experiment shows that the computation accuracy of the free term coefficient is very high for various bodies even with edges and corners, and the convergence speed is high for the Cauchy principle value integration from different meshes. Based on the method a numerical model for wave diffraction and radiation from three dimensional bodies is developed. Comparison is carried out with analytic solutions for wave forces on uniform and truncated cylinders. It shows that the wave forces from the present model converge quickly to the analytic solutions. 8 Study on Fast Integration Method for Bessho Form Translating-pulsating Source Greens Function Distributing on a Panel bJTN{N1) Yao Chaobang, a PhD candidate in marine hydrodynamic. His PhD project is doing some research on the fast evaluation method for 3-D translating and translating-pulsating Green s function, meanwhile, apply these functions for calculating wave-making and seakeeping performance of two ships parallel to each other. 2) Dong Wencai is Professor in hydrodynamics at Naval University of Engineering, doctoral supervisor. Dong is director of academic committee of Aeronautical Science Key Laboratory of high speed hydrodynamic. His current research and project activities include topics related to seakeeping performance of ship, ship-ship interaction, and drag reduction of high speed crafts by air-cavity. Q[The singularities, oscillatory performance of the panel source functions, which are derived by using a single integral expression of Bessho form translating-pulsating source Green s function, are analyzed. Relative numerical integral methods such as LOBATTO rule, variable substitution and steepest descent integration method are used to evaluate this type of Greens function. An improvement of the computation method of the Greens function based on the numerical steepest descent method whose complex domain is restricted only on the  EMBED Equation.DSMT4 -plane is introduced. The integral along the real axis is computed by use of the variable substitution method to improve the efficiency. Contour integral technique is adopted, also, a fast method for justifying the relative positions of singular points and integral contour is established based on Greens theorem. The numerical method is validated by the comparison with other existing results, and is shown to be efficient and reliable in the calculation of the velocity potentials for the three-dimensional seakeeping and hydrodynamic performance of floating structures moving in waves. 9 Numerical simulations of nonlinear wave interactions with structures based on the Arbitrary Lagrangian-Eulerian finite element method bJTN{Nsd-N 1999t^NS-Nt]'Yf[96~girT6R NNZSXf[MO 2006t^&Ofe'Yf[:gh] z|{AmSORf[NNZSXf[MO s:NYm_l'Yf[wm myf[N] zf[|oRYec0 Q[  In simulations of flow viscous free surface, the Arbitrary Lagrangian-Eulerian (ALE) finite element method (FEM) is a powerful tool, and it has been widely applied to solve viscous flow with free surface since 1980s. In this method, the computation mesh is not fixed and does not depend on the fluid particle. The mesh can move arbitrarily relative to the coordinate and can avoid node clustering. In this work, The ALE FEM is employed to analyze interactions between nonlinear waves and structures and the fractional step method is used to solve free surface Navier-Stokes flow. The velocity on the free surface is updated by the Lagrangian method and the mesh velocity in the fluid domain is obtained through a linear interpolation according to the velocity on the free surface. Numerical cases including free oscillation of a wave in a container, solitary wave impacting on a vertical wall and two solitary waves colliding are simulated, and results are compared with analytical solutions, fully nonlinear solutions by potential theory and experimental results to show the present numerical method is efficient and accurate for wave-body interactions. 10 Oscillations of Elastically Mounted Cylinders in Regular Waves bJTN{NypglYec -Nq\'Yf[ZSXu[^ N-Nq\'Yf[]f[b^(uRf[N] z|;NN -Nq\'Yf[] zRf[xvz@boR@b ^Nwя\wm m] z͑p[[oR;NN |QN-NVwm m] zf[O8^RtN -NVRf[f[OAmSORf[NNYXTOTsXRf[NNYXTOYXT ^NwRf[f[OoRtN|QNVEBg_ 0Engineering Applications of Computational Fluid Mechanic *. , B H X j l n r t o ͿulXXuPAhhweCJaJnH tH hhweo('hbV3hweCJOJQJaJmH o(sH hweCJaJo(&hbV3hwe5CJOJPJQJaJo(hbV3hweCJaJo(h+vhwe5aJo(h+vhwe5CJaJo(h1hwe5B*\o(phh1hwe5B*\phh+vhwe5B*\phh+vhwe5B*\o(ph hwe5o(hthwe5CJ aJ o( n l  K <=u"##h7$8$H$WD`hgdwegdwed7$8$H$WD`gdwe d7$8$H$gdwedhgdwe 7$8$H$gdwe $dha$gdto p BDlnvx ,|ļxxfVh+vhwe5CJPJaJo("h+vhwe5CJOJQJaJo(h1hweCJaJo(h+vhwe5CJaJo(h1hwe5\o(h1hwe5\h+vhwe5\h+vhwe5\o(hwe5\o(hweCJaJo($hhweCJOJQJaJnH tH hhweCJaJnH tH hhwe6CJaJnH tH J45;٪مt`&j,+U hbV3hweCJUVaJo(!j)hbV3hweCJEHUaJ&j&+U hbV3hweCJUVaJo(!jhbV3hweCJEHUaJ&j,U hbV3hweCJUVaJo(jhbV3hweCJUaJhbV3hweCJaJo(hbV3hweCJaJhbV3hweCJPJaJhbV3hweCJPJaJo(567=>U`ajwĹ߹߭߹tc߭߹O&j+U hbV3hweCJUVaJo(!j hbV3hweCJEHUaJ&j+U hbV3hweCJUVaJo(!j hbV3hweCJEHUaJ&jb+U hbV3hweCJUVaJo(hbV3hweCJaJo(hbV3hweCJaJhbV3hweCJPJaJo(hbV3hweCJPJaJjhbV3hweCJUaJ!jhbV3hweCJEHUaJ   C߀l[Gә߀&hbV3hweCJH*OJQJ^JaJo(!j\hbV3hweCJEHUaJ&j,U hbV3hweCJUVaJo(hbV3hweCJaJhbV3hweCJPJaJo(hbV3hweCJPJaJhbV3hweCJPJaJhbV3hweCJPJaJo(#hbV3hweCJOJQJ^JaJo(hbV3hweCJaJo(jhbV3hweCJUaJ!jhbV3hweCJEHUaJ'.<=>UVWXY   ̺̯}i̯UD8hbV3hweCJaJo(!j>hbV3hweCJEHUaJ&j+U hbV3hweCJUVaJo(&hbV3hweCJH*OJQJ^JaJo(!jhbV3hweCJEHUaJ&jA,U hbV3hweCJUVaJo(hbV3hweCJPJaJhbV3hweCJaJ#hbV3hweCJOJQJ^JaJo(jhbV3hweCJUaJ!jhbV3hweCJEHUaJ&j,U hbV3hweCJUVaJo(IJT)4^ƶᢓo^SSSSDjhbV3hweCJUaJhbV3hweCJaJ hbV3hweB*CJaJo(ph!hbV3hwe0JB*CJaJph$hbV3hwe0JB*CJaJo(phhbV3hweB*CJaJph&jhbV3hweB*CJUaJphhbV3hweCJOJQJaJo(hbV3hweCJPJaJo(hbV3hweCJPJaJ#hbV3hweCJOJQJ^JaJo(hbV3hweCJaJo(!'2inos|pddddSd!jF'hbV3hweCJEHUaJhbV3hweCJaJo(hbV3hweCJH*aJ!j\$hbV3hweCJEHUaJ&j+U hbV3hweCJUVaJo( hbV3hweB*CJaJo(phhbV3hweB*CJaJphjhbV3hweCJUaJ!j!hbV3hweCJEHUaJ&j,+U hbV3hweCJUVaJo(hbV3hweCJaJ;<=Jt   F L v x !!!!"""""" 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The responses of the cylinders induced by wave excitation are determined by the equations of motion coupled with the solutions of the wave radiation and diffraction problems. Experiments for three-cylinder cases are then designed and performed in a wave flume to determine the accuracy of this method for regular waves. The response amplitudes of the cylinders in regular waves were record. Comparison of the calculated results with experimental values is acceptable. It is found that that the response curves differ significantly from that of a single cylinder because the interactions between the cylinders modify the diffraction and radiation forces. The paper may offer some insights into such resonant phenomena in wave diffraction problems. 11 Some annotations and comparisons on Green function calculation and application for vessel motion bJTN{NRenchuan Zhu, received his BS and MS degrees from China (Anhui University and Dalian University of Technology) and his PhD from Japan, Hiroshima University. He had worked Hiroshima University and George Mason University for one year and four months respectively as a visiting Scientist. He joined Shanghai Jiao Tong University in 2002 and was promoted to full professor in 2009 in the Department of Naval Architecture and Ocean Engineering. Renchuan s teaching and research are in ship motions theories and hydrodynamics of both ship and floating structures. Recently he is focusing time domain simulation for ship and floating structure in waves by both potential and viscous method and the hydrodynamic problems related to deepwater mooring system, offshore installation. He has published over 80 journal articles and is a reviewer for many different journals. Q[ : Green function calculation is the key problem to analyze hydrodynamics and motions for vessel. The calculations and applications of Green functions for vessel moving with/without forward speed both in time domain and frequency domain, and the newly derived oscillating source Green function in the water where the water density linearly varying with water depth are outlined. The comparison of hydrodynamics and vessel motions are carried out by using frequency domain Green function. Error annotation of frequency results is obtained compared to the experimental ones. The numerical calculation and comparisons of retard function for time-domain analyzing floating body in waves are conducted by the direct time-domain method (DTM) and the transformation method from frequency to time-domain (FTTM). A Wigley-hull-form ship and a cylindrical platform floating in waves are analyzed and verified, and the corresponding retard functions are in good agreement by the two methods. A Program is developed by the hybrid method of transient Green function and simple Green function to eliminate the divergence due to ship flare. The fluid field is decomposed into inner and outer domain. Rankine source is applied in the inner domain while transient Green function is adopted in the outer domain and they re matched on an imaginary vertical surface. The numerical results of ship motions of Series 60 and S175 ship at forward speed are presented and discussed. They are also compared with those of other methods or available experimental data, and show good agreement. 12 Numerical Calculation of the Far-field Waves Generated by High-speed Ships in Finite-Depth Water bJTN{Ne^Yec NwmN'Yf[ZSXu[^ 1996t^2002t^02005t^2011t^fN,{22J\023J\025J\026J\VE9`lOITTC d~'`b/gYXTOYXT s:N-NV 9] zf[O96Rf[f[/gYXTOYXT0-NVRf[f[OAmSORf[NNYXTO4lRRf[NN~~XT0-NV*wmf[OQl96~vNNYXTOYXT0_V 9b/gOSOSTG OXT 04lRRf[xvzNۏU\ 0Journal of Hydrodynamics gbLY Ship Technology Research_V 0International Journal of Naval Architecture and Ocean EngineeringV 0 0-NV 9 00 096Rf[ 0T 09wm] z 0Y0 Q[ : When solving the wave making problem under the framework of potential flow, two choices of the Green functions are the Havelock source and the Rankine source.Compared with the Havelock source, Rankine source holds a simple form and can offer a flexible manner for satisfying the boundary condition. But the Rankine source suits only for solving the near-field waves generated by the ships. A large free surface computational domain means a large number of free surface panels, which is not favorable. In this study, a combined Rankine/Havelock source method is used. The near-field Kelvin wave systems generated by the high-speed displacement-type ships are computed using Rankine source panel method. The far-field wake waves are then determined numerically by equivalent singularity distributed on the central longitudinal section of the ship. The principle and numerical treatment of the equivalent-singularity-distribution method are introduced and the numerical tests are applied to the shallow water case. 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