Original scientific paper A mixed numerical formulation, based on the method of characteristics (MOC) and finite difference method (FDM), is proposed for the computational simulations of hydraulic transients.To include the effects of unsteady friction, i.e. the contribution of unsteady behavior of wall shear stress, the numerical algorithm includes the Brunone friction model.The governing water hammer equations are discretized by MOC and the discretization of the local and convective acceleration term in the unsteady friction model is conducted by FDM.The procedure results in an explicit-implicit time marching scheme used for predicting the unknown values of piezometric head and discharge from the known initial conditions.The resulting system of equations is resolved in an iterative fashion.Due to its relatively low complexity, the obtained numerical algorithm is attractive for computational implementation.At the end of the paper a few illustrative numerical examples are presented, compared with available experimental data, and discussed.
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Travaš et al. (2015) studied this question.