Water Hammer and Hydrodynamics’ Instability - Advances in Control and Automation of Water Systems - page 65

figure 4.3 Coordination of (s-t).

figure 4.4 Coordination of (s-t) for finding P and V.

At each interior solution point, signals arrive from the two adjacent points simulta-
neously [2-5]. A linear combination of H and V are invariant along each characteristic
if friction losses are neglected. Therefore, H and V can be obtained exactly at solution
points. Head losses concentrated at solution points. The assumption is the friction is
small. Transient modeling essentially consists of solving these equations. These equa-
tions are applied for every solution point and time step. It is valid for a wide variety of
boundary conditions and system topologies.