General equations of the scheme

img000001750000000100000000.jpgFigure 26

Let: Dfi = fA’ - fA fA = fi

Dfj = fB’ - fB fB = fj

The expression of a function in M may be written as:

fM = (1-Q) + Q

fM = + (Dfi + Dfj) [31]

The derivative () at point M is written as:

()M = (1-Q) + Q

=> ()M = + Q [32]

The derivative () at point M is written as:

()M = ( + )

=> ()M = [33]

Equations [31], [32] and [33] are used to discretize St. Venant’s equations.