points where two subregions overlap, has been used for the grids that cover 

 the computational and fluid regions. There are 34 equally spaced grid points 

 on the half -body contour. At the far right vertical boundary, at the bottom 

 horizontal boundary, and at the vertical boundary below the body, grid points 

 position themselves in a way that makes the mesh near these boundaries 

 orthogonal. At the far right boundary there are 25 grid points; at the bottom 

 boundary, 102 grid points; on the vertical boundary directly beneath the 

 body, where a symmetry condition is specified as a wall condition, 18 points. 

 The initial distribution of grid points on the free surface is arranged so 

 that the mesh near the intersection of the free surface and the body is 

 approximately uniform in both the x- and y-directions (Fig. 6), and the mesh 

 near the intersection of the free surface and the far right boundary is also 

 approximately uniform in both directions. There are 90 grid points along the 

 free surface. 



The iteration for the solution to the Laplace equations for the changing 

 mesh and for the velocity potential is done simultaneously. It is found that 

 the mesh does not change greatly from time step to time step and hence a test 

 for the convergence of (J) suffices. This convergence test is that the square 

 root of the sum of the squares of the residuals at the 34 body points should 

 be less than 0.001. A spot check of the solution iterates indicated that the 

 relative change in ({> near the body was about 0.1 percent when the criterion 

 was satisfied. 



For the solution of the Laplace equations, an overrelaxation factor of 

 1.4 was chosen for grid points inside the computational region. For grid 

 points on the body, where a Neumann boundary condition is specified, such a 

 large relaxation factor caused instabilities in the solution process for (j). 



19 



