wetted length of the body given by x = Bx(a,t) and y = By(a,t) where 

 - it/2 < a < a^Ct). (The function a^Ct) depends on the position of the 

 intersection of the free surface and the body contour.) 



NUMERICAL SCHEME 



The functions xp(e,t), yp(e,t), (|)p(e,t) along the free surface and 

 xg(e,t), yg(e,t) along the body contour obey five coupled first order 

 differential equations in time with specified initial conditions. In 

 addition, the velocity potential must satisfy specified boundary conditions at 

 all times. To solve these equations a finite-difference method is used. 



BOUNDARY FUNCTIONS 



Each of the five boundary functions is discretized with respect to time 

 and space using a fixed time step At. The discretized forms of the functions 

 are denoted by 



x^") = xp(e., nAt) (20a) 



Fj * J 



y^"^ = 71.(61. nAt) (20b) 



Fj J 



<j,(n) = <J,T,(e., nAt)- (20c) 



Fj * J 



for j = 1, . . . , N, and 



x("> = x^(e,, nAt) (20d) 



Bk 



^B'^'^k' 



10 



