L Length scale 



M Number of body grid points 



m,n Time levels 



N Number of free-surface grid points 



n(a,t) = (njj,ny) Outward directed unit normal on body contour at 

 (Bx(a,t),By(a,t)) 



Origin of Cartesian coordinate system 



p Dimensionless pressure = p'/po^L^ 



p' Dimensional pressure 



s Arclength along the body contour 



t Dimensionless time = t 'o 



t' Dimensional time 



x,y Dimensionless Cartesian coordinates = (x',y')/ L 



x',y' Dimensional Cartesian coordinates 



xgCe.t) ,yB(e,t) Functions describing position of fluid particles along 

 body contour 



xp(e,t) ,yp(e,t) Functions describing free-surface position 



XQ,yQ Coordinates of moving center of body 



u,v Velocity of a fluid particle; u = ^^, v = (j)y 



Vn(a,t) Normal component of body-contour velocity (positive 

 outward) at (xgCa.t), ygCa.t)) 



w Half-width of the rectangular fluid region 



a,3,Y Functions of (^.n) describing the mapping of the fluid 

 region onto the computational region 



A Laplace operator 



At Time increment 



6^ Phase angle of first-order force on heaving body 



62 Phase angle of second-order force on heaving body 



