Ahmadi Azadeh


Water hammer analysis by finite element with complex boundary conditions

Student Name

Azadeh Ahmadi




Mohammad Reza Chamani
(Assist. Prof._Civil Engineering Department_Isfahan University of Technology)


Keyvan Asghari
(Assist. Prof._Civil Engineering Department_Isfahan University of Technology)









Nowadays, the finite element method is a strong tool for solving engineering problems. In this study, the finite element method is used to solve water hammer problems with complex boundary conditions. Two methods, standard Galerkin (G) and Petrov Galerkin (PG) are used for modeling this phenomenon. Boundary conditions contains reservoirs at upstream and downstream, pump with constant velocity, closing valve at downstream, shut-off pump at upstream, air chamber, surge tanks and series pipes. The results are compared with the characteristics method predictions.

It is shown that PG method simulates all conditions better than G method. The effects of parameters such as explicit or implicit parameters for solving (q), damping factor (e), number of elements and time step are investigated. If the value of q approaches zero, results diverge and if it approaches one, rapid changes of pressure head are not modeled well. Increasing the number of elements improves the results, but causes to increases the time of simulation. Increasing the value of e improves the results. Using the courant condition for choosing the time step, the results are in agreement with the results characteristics method. In all conditions, the finite element method results are close enough to the results of characteristic method.