street^ Chan and Fromm 



Fig. 8. Irregular star for p calculations 



The hypothetical particles that mark the free surface are 

 moved to their new locations according to their locally interpolated 

 values of u and v. For a given particle k we find the velocity 

 component u,j for the particle by making a Taylor series expansion 

 about the nearest data point of the u field. Similarly, a series 

 expansion about the nearest data point of the v field gives v^, the 

 y-component of the particle velocity. With U|, and Vj^ available, 

 each free surface marker particle is advanced by the following 

 formulas: 



n+l n 1 n+l c. 



^k =^k'^^k ^* 



n+l 



.n+l 



(45) 



\ = ^k ^ ^k ^' 



where xjj and yJJ refer to the position of the k^ particle at the 

 n*^ time step. Also, the particle velocities are evaluated at the 

 advanced, i.e., n+l , tlnne step. 



The quantities u and v are not defined outside the fluid 

 domain, but they are needed to carry out the computations using 

 Eqs. (37) and (43) and the particle velocities near the free surface. 

 We calculate these undefined u and v values by a simple linear 

 extrapolation from the fluid interior. 



A complete set of initial data -- the u and v fields and the 

 position of a line of particles depicting the free surface, are needed 

 to start the computation. The initial pressure p needs to be known 

 only approximately, such as a hydrostatic distribution, because the 

 p field is solvable if u and v are given. 



174 



