street^ Chan and Fromm 



and 



Here, p is the pressure; g^ and gy are the x and y components 

 of the gravity acceleration whose absolute value is g and t is the 

 time variable. Also, if the direction of gravity is the same as the 

 -y direction, then gx = a-nd gy = - 1, 



Boundary conditions are easily derived for the fluid motion at 

 the solid walls of the tank (cf. , Chan and Street [ 1970a] ). For incom- 

 pressible fluids with very low viscosity, such as water, it is suffi- 

 ciently accurate to use at the free surface the single condition 



p = Pa(x,t) (36) 



where pg is the externally applied pressure at the free surface. 

 Under usual circumstances Pq = , but it can also be prescribed as 

 a function of x and t for some problems. 



As shown in Fig. 7 the computation region is divided into a 

 number of rectangular cells. The fluid pressure p is evaluated at 

 the cell centers, while u is defined at the mid-point of the right-hand 

 and left-hand sides of the cell and v is defined at the mid«point of 

 the upper and lower sides. Then, for the cell (i,j) the following set 

 of equations are derived from Eqs. (33) and (34): 



^-^j =^i4i ^5tg,+-g^(Pi.,j -PiP 

 n+l * J. c^ _L 8t / \ 



(37a) 

 (37b) 

 (37c) 

 (37d) 



In the above equations, variables with the superscript n+l 

 are related to the n + l*** time step. Variables lacking a superscript 

 are evaluated at the n*^ step. Thus, Eqs. (37) are suitable for 

 updating the values of u and v about the cell (l,j). The "eonvective 

 contributions" u* and v* are 



172 



