This note proposes a new quasi-two-dimensional (quasi-2D) numerical scheme for simulating a water hammer that significantly reduces the computational burden compared to two existing quasi-2D schemes, as numerically demonstrated in this note by application to a reservoir-pipe-valve system. Computational cost is decreased through using one-dimensional (1D), rather than two-dimensional equations for pressure head and discharge and using a staggered grid with half of the computational nodes compared to a rectangular grid. It is valid to use the proposed 1D characteristic equations for the pressure head and discharge, as it is proved that these yield identical results to explicit quasi-2D solution procedures previously introduced in the literature.

The soil conservation service curve number (SCS-CN) model is a widely utilized tool for estimating runoff and relies on two empirical parameters: the CN and the ratio of initial abstraction to maximum potential retention (λ). The determination of the parameters is via the empirical method or calculations based on actual data. However, few studies address the effect of rainfall on parameter selection, and collecting runoff data for model analysis is challenging. This study, taking the Nemor River Basin as the research region, investigates how the combination of CN and λ impacts the model in different rainfall conditions. Using runoff plots and reanalysis product data, the study reveals that: (1) the calculated methods outperformed the empirical method, increasing the Nash Sutcliffe efficiency coefficient from 0.34 to 0.65. (2) A higher λ value (0.2 compared to 0.02) reduces runoff and smoothes the runoff curve, which becomes less obvious with increasing CN. (3) The CN values exhibit a non-monotonic relationship with rainfall, initially decreasing before rising, highlighting the need to adjust the CN based on rainfall. Moreover, the SCS-CN model's performance with reanalysis data approximates that with actual data, confirming the viability of reanalysis datasets in this region.

A stepwise method is one of the efficient approaches in the calibration of transient flow in viscoelastic pipes. However, there is the lack of comprehensive research on the calibration method for retarded time and creep compliance. Therefore, the sensitivity of the order of magnitude of the creep parameters in the presence of interactions to transient flow pressure damping and phase in the case of the two-element Kelvin–Voigt model is investigated. Also, the calibration methods of retarded time and creep compliance in the stepwise method of transient flow parameter calibration for viscoelastic pipes are proposed. The results indicate that the creep compliances do not affect the phase of the pressure fluctuations when the selected retarded times are greater than the order of magnitude 10−1. For the first Kelvin–Voigt element, when the order of magnitude of the retarded time exceeds 10−2, an increase in creep compliance results in an increase in the degree of damping of pressure fluctuations. When the order of magnitude of the retarded time is less than 10−2, the rule is reversed. For the second Kelvin–Voigt element, an increase in creep compliance results in an increase in the degree of damping of transient flow pressure fluctuations independent of the retarded time.

Hydraulic analysis of steady state conditions is typically used in the design and operation of gas networks. However, operational gas network systems are never in the steady state as demands and pressures vary with time. By comparison, transient analysis is more valuable and helpful for engineering design and operational management. The method of characteristics (MOC) is often used to analyze the transient flow of gas networks because it has clear physical concepts and employs rigorous mathematical analysis and precision in calculation. However, with MOC a small time step has to be included for an accurate result, which costs a lot of computing time. In this paper, it is shown that the method of characteristics with an inertial multiplier is capable of providing a numerical simulation of the transient flow in gas networks. After the inertial multiplier is established, then the transient flow for a gas network system is numerically simulated. Two simulation outcomes are compared, one using the method of characteristics and another the method of characteristics with an inertial multiplier. Results show that the time step can be selected flexibly and the computational speed can be reduced by means of the method of characteristics with an inertial multiplier. The method of characteristics with an inertial multiplier is more efficient for transient analysis of gas networks than the method of characteristics alone.

Accurate simulation of cavitating flows in pipeline systems is important for cost-effective surge protection. However, this is still a challenge due to the complex nature of the problem. This paper presents a numerical model that combines the discrete vapor cavity model (DVCM) with the quasi-two-dimensional (quasi-2D) friction model to simulate transient cavitating flows in pipeline systems. The proposed model is solved by the method of characteristics (MOC), and the performance is investigated through a numerical case study formulated based on a laboratory pipeline reported in the literature. The results obtained by the proposed model are compared with those calculated by the classic one-dimensional (1D) friction model with the DVCM and the corresponding experimental results provided by the literature, respectively. The comparison shows that the pressure peak, waveform, and phase of pressure pulsations predicted by the proposed model are closer to the experimental results than those obtained by the classic 1D model. This demonstrates that the proposed model that combines the quasi-2D friction model with the DVCM has provided a solution to more accurately simulate transient cavitating flows in pipeline systems.