Improved third-order weighted essentially non-oscillatory scheme for transient pipe flow with unsteady friction

Accurate simulation of water hammers is essential for pipeline system stability and component protection. This paper proposes an improved third-order weighted essentially non-oscillatory (WENO) scheme integrated with the finite volume method (FVM) to solve one-dimensional water hammer problems. The proposed scheme refines accuracy by enhancing the global smoothness indicator through detailed decomposition and Taylor series expansion, introducing a dissipation-regulating parameter p. Two unsteady friction models are incorporated to further improve predictions. Comparisons with first- and second-order Godunov schemes and classical WENO-JS and WENO-Z schemes demonstrate that the proposed method maintains high accuracy while exhibiting superior shock-capturing capabilities. The method effectively suppresses spurious oscillations and minimizes numerical dissipation where traditional methods falter. With unsteady friction included, simulated pressures align excellently with experimental data, confirming the scheme’s effectiveness and reliability. These results highlight the method’s potential for complex pipeline system simulations.