In each cell of a mesh it is customary to use only one value for each dependent variable defining the fluid state. The use of several points in a cell to define the region occupied by fluid, therefore, seems unnecessarily excessive. Suppose, however, that we define a function F whose value is unity at any point occupied by fluid and zero otherwise. The average value of F in a cell would then represent the fractional volume of the cell occupied by fluid. In particular, a unit value of F would correspond to a cell full of fluid, while a zero value would indicate that the cell contained no fluid. Cells with F values between zero and one must then contain a free surface. Thus, the