A SECOND ORDER STATIONARY SOLUTION OF THE THREE DIMENSIONAL WAVE DIFFRACTION POTENTIAL

A theory on the second order wave diffraction by a three dimensional body fixed in a regular sea has been developed in the present paper. By regarding the sinusoidal disturb potential as a stationary solu- tion of an initial value problem, and using Laplace transformation method and Tauberian theorem, the boundary value problems of stationary solution of the first and second order diffraction potential have been de- rived in this paper. Furthermore, the explicit solution of the second order stationary diffraction potential has been obtained with the method of the double Fourier transformation. It is found that the asymptotic behaviour of the second order stationary solution at far field is dependent on two wave systems, the first is 'free wave', travelling independently of the first order wave system, the other is 'phase locked waves', which accompany the first order waves. At the same time, the radiation conditions of the second order diffraction problems are derived. We also find that one can still pursue a steady state formulation with the inclusion of Rayleigh damping. Finally, as an example, the second order wave forces upon a fixed vertical cir- cular cylinder have been calculated, and the numerical results agree well with the experimental data.

WATER SURFACE WAVE RADIATION GENERATED BY MULTIPLE CYLINDERS OSCILLATING WITH IDENTICAL FREQUENCY

The water surface wave radiation problem caused by multiple cylinders oscillating with identical frequency was solved in frequency domain by the boundary element method using simple Green's function in the inner water region combined with the eigenfunction expansions in the outer water region. The numerical method is suitable to the situation of constant depth of outer regions and complicated boundary conditions of inner region, while the oscillating modes, motion amplitudes and phases of the cylinders may be different from one another. The second order potential and hydrodynamic forces acting on each cylinder were evaluated completely by perturbation method. Compared with the case of single oscillating cylinder, hydrodynamic interference phenomena, such as wave resonance and negative added mass, of the radiation problem due to the oscillatory motions of multiple cylinders are identified which is of engineering importance to the design of moorings and other facilities involving multiple structures.

Theory and application of numerical simulation method of capillary force enhanced oil production

A kind of second-order implicit upwind fractional step finite difference methods are presented for the numerical simulation of coupled systems for enhanced （chemical） oil production with capillary force in the porous media. Some techniques, e.g., the calculus of variations, the energy analysis method, the commutativity of the products of difference operators, the decomposition of high-order difference operators, and the theory of a priori estimate, are introduced. An optimal order error estimate in the l2 norm is derived. The method is successfully used in the numerical simulation of the enhanced oil production in actual oilfields. The simulation results are satisfactory and interesting.

THE SECOND-ORDER HYDROELASTIC ANALYSIS OF A SWATH SHIP MOVING IN LARGE-AMPLITUDE WAVES

Based on the second order hydroelasticity theory of ships, the numerical methods and the calculated results of the non-linear hydroelastic responses of a ship traveling in rough seas were investigated. The non-linear hydrodynamic actions induced by the rigid body rotations and the variations of instantaneous wetted surface area were included in the second order analysis. The first order wave potentials and responses, which are sure to make the major contributions to the second order hydrodynamic actions, were obtained by employing the translating and pulsating source Green function and the Kelvin steady wave flow solution based on the linear three-dimensional hydroelasticity theory. The influences of the forward speed and the steady wave flow on the responses, and the differences of the predicted non-linear responses were illustrated by the numerical examples of a SWATH ship traveling with forward speed of 12 kn in irregular waves.

A METHOD FOR THIRD ORDER FORCE ON AXISYMMETRIC BODIES

This paper develops a third order diffraction theory for the third order wave loads. Our method has been implemented for bodies of revolution with vertical axes, but the theory is also available for arbitrary bodies. Numerical tests were made to validate the numerical code by comparing the third order force with some published ones on a uniform cylinder. The method has also been used to compute the third order moments on a uniform cylinder and third order forces and moments on a truncated cylinder.

SECOND ORDER DIFFRACTION FORCES ON HORIZONTAL CYLINDERS

The second order diffraction forces on a floating semicircular cylinder and a submerged circular cylinder are calculated using the method of Lighthill(ref.3). The first order potential is obtained by the multipole expansion and numerical results are provided.

A NUMERICAL METHOD FOR SECOND ORDER MEAN FORCES AND SLOWLY VARYING FORCES ON A FLOATING STRUCTURE

Existing far field expressions of second order potentials are by no means complete.Hence there has been no exact far field expression of second order potentials.In this paper the far field expression for Φ_d^((2)) is purposely avoided in deducing the formulae of second order forces and a series of functions Φ_(dRn)^((?)) are used.The far field expression of is given,which for (x,U,z)∈Σ,φ_(dRn)^((2))(?) φ_d^((2)).Using these properties formulae for calculating second order diffraction forces are obtained.To calculate the integral ∫∫_(?)1/g f_(?)Ψ_(?)ds it is divided into two parts.One is the integral over a finite domain and the function under the integral is continuous,so the usual approximate integration formulae may be used. The other is the integral over an infinite domain.Using the far field expression of first order potentials,formulae for calculating the integral to meet given accuracies are given. The mooring force in surge direction is used for comparison between numerical predictions and experimental measurements.The predicted results are checked against the measured value in a specially designed test.In the low frequency domain of interest,the mooring forces in surge,for calculated and experimental spectra are in good consistency so long as the damping coefficients is choosen appropriately.