Hydraulic behavior modeling of the simple tank using the Finite Difference Method: a comparison of four different methods

In this paper, the hydraulic modeling of a simple surge tank with two assumptions of with or without friction condition at both gradually and suddenly valve closing is studied. The four different kinds of the finite difference method called the Explicit Euler, Implicit Euler, Predictor-Corrector Euler and Rung-Kutta methods are used to solve hydraulic equations and the results are presented and compared. Comparison of the results shows that in all cases, by using the Implicit Euler method, the fluid level variation is less than other available methods. In other words, the fluid level variation obtained using Implicit Euler is about 3 percent less than that obtained using Rung-Kutta method at without friction condition. In addition, at friction condition, the fluid level variation obtained using Implicit Euler is about 4, 3 and 2 percent less than that obtained using Explicit Euler, Predictor-Corrector Euler and Rung-Kutta methods, respectively. Moreover, the results converge faster than the other methods at without friction condition using Implicit Euler method and finally the results converge faster than the other methods at friction condition using Rung-Kutta method.