Embedded Modified Euler Method: An Efficient and Accurate Model for Dynamic Simulation of Pipe Networks

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 nonlinear algebraic equation in terms of the reservoir head and inflow. These equations are then embedded into the nonlinear system of equations describing the steady state flow in the pipe network to obtain the final system of equations. A Newton-Raphson method of linearization 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 equation automatically yields the distribution of nodal heads along with the reservoir head at the end of each period. The method only uses one steady state simulation per period to accurately and efficiently predict 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 conventional