Embedded modified Euler method: an efficient and accurate model Available to Purchase

In this paper, an efficient and accurate method for the extended period simulation of pipe networks under dynamic loading is proposed. The method uses the modified Euler method to discretise the ordinary differential equation governing the variation of water level in the reservoirs to yield a non-linear algebraic equation in terms of the reservoir head and inflow. These equations are then embedded into the non-linear system of equations describing the steady-state flow in the pipe network to obtain the final system of equations. A Newton–Raphson method of linearisation is used for the equation governing the tank water level variation along with a gradient formulation of the pipe networks. The solution of the resulting system of equations automatically yields the distribution of nodal heads along with the reservoir head at the end of each period. The method uses only one steady-state simulation per period to predict accurately and efficiently the reservoir water elevation. Application of the proposed method does not require special coding and can be easily embedded into the existing pipe network simulation codes. The method is applied to four test problems and the results are presented and compared with those of a conventional extended period simulation method and some other existing methods. The results show that the proposed method is considerably more accurate than the conventional algorithm and more efficient than existing improved methods of dynamic simulation.