Interpolation schemes in the Method Of Characteristics for water hammer problems with complex boundary conditions
Mohammad Reza Chamani
Complex Boundary Conditions
Method of Characteristics (MOC)
In this research, different interpolation schemes in the Method Of Characteristics (MOC) were used for water hammer problems. Governing equations of water hammer were solved using the complete and approximate method of characteristics, considering complex boundary conditions. In addition to the interpolation schemes used in the literatures, cubic-hermite nonlinear interpolation was used for the first time. After discritization the governing equations and computer programming, several models were selected for validation. In some models, numerical results were compared with experimental results. In addition, the effects of courant number on the results were investigated. Both linear and nonlinear interpolation schemes show that the difference between results of using complete or approximate equations are small and can be ignored. In all schemes, approximate equations needs less CPU time to process. It is shown that space and time-line interpolation, in linear and nonlinear methods, achieved better solution compared to hybrid interpolations. By decreasing the Courant number, nonlinear interpolation schemes lead to more accurate results than the linear ones. Among nonlinear methods, hermite method shows fewer numerical errors in comparison with spline method. The comparison indicates that nonlinear methods have less phase difference with measured results, and in nonlinear methods, hermite scheme results are closer to experimental results. Decreasing the courant number decays the accuracy of results, especially in linear methods. Space-line interpolations are less sensitive to the variation of courant number than time-line ones. The results of different models show that for the complex boundary conditions used in this work, the choice of interpolation scheme is not crucial and linear interpolations are recommended, because of less computational costs. Energy approach is also used to compare numerical errors of different interpolation Schemes, which show less error in nonlinear methods, especially in the hermite scheme. Altogether, comparison of accuracy of different interpolation schemes shows that time-line interpolations are the best method; however, these schemes require more time and computer capacity in comparison with space-line schemes. In the models investigated in this work, cubic-hermite scheme reveals the most accurate solution.