Numerical simulation of water hammer using implicit Crank-Nicolson Local Multiquadric Based Differential Quadrature

Abstract

This paper focuses on developing a numerical model based on Implicit Local Multiquadric Based Differential Quadrature Method for simulation of water hammer phenomena in a pipeline system consisting of a valve, pipe and surge tank. This model is used with the aim of reducing computational costs and increasing accuracy. After brief interdicting of governing equations of water hammer, the spatial and temporal derivatives are implicitly discretized by the Local Multiquadric Based Differential Quadrature and Crank Nicholson scheme, respectively. The system of governing equations of the water hammer is discretized in matrix form and solved by applying appropriate boundary and initial conditions. The proposed model is verified by two experimental case. The comparison between obtained results and experimental reported data indicates that the presented method is in good agreement with experimental observations. To evaluate the computational cost, these examples were also solved concurrently with Method of Characteristics. The comparison showed that this method is able to simulate the water hammer more accurately despite less computational effort. It is also found the accuracy of the model depends on the Courant number. However, the model maintains its stability in Courant numbers more than the one.