A nonlinear time.4omain hybrid method for simulating the motions of ships advancing in waves

Numerical simulation of large amplitude ship motions and applications to ship design and safe operation

“…The validated TDGF method is used to find the matching surface condition, which is a precious heritage from the first step in this thesis study. Furthermore, the matching is fixed in space, i.e., v n =0 in equation 2-10and equation (2)(3)(4)(5)(6)(7)(8)(9)(10)(11), so that the difficult-to-treat waterline integral term trivially vanishes.…”

“…Similar trend has also been observed by other researchers (Kataoka et al, 2002). What"s more, the deviation between the results from traditional differential method and integral method is obvious, which indicated the necessity to employ the concept of integrating form expression (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15) when dealing with the large-amplitude problems.…”

“…Since k 1 wave system is neglected, only the weighting functions for k 2 wave system have been shown. The weighting functions are defined by the following expressions: Figure 2.21 shows the non-dimensional Kochin function amplitude in the range α 0 < θ < π and Figure 2.22 shows the integrand of the second term in expression (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19). A more detailed analysis can be seen in Naito, et al (1988).…”

“…The second approach is based on a frequency domain 3D panel method NEWDRIFT for the solution of potential calculation. The deduced first-order results either from the time-domain or the frequency domain approach are introduced in equations 2-22and 2-23for the calculation of the Kochin functions, from which the added resista nce is calculated according to equation (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19).…”

“…In the outer domain II, the transient time-domain Green function is employed to solve the disturbed potential on S c . The integral equation is expressed as: (p S c ) (3)(4)(5)(6)(7)(8)(9) In the present formulation, the matching surface is fixed, thus V N is essentially zero and the last integration term on the waterline vanishes. (3)(4)(5)(6)(7)(8)(9)(10) The velocity potential in the inner domain can also be expressed by a simple source distribution, namely as:…”