Hydraulic Transient Analysis of Sewer Pipe Systems Using a Non-Oscillatory Two-Component Pressure Approach

On the basis of the two-component pressure approach, we developed a numerical model to capture mixed transient flows in close conduit systems. To achieve this goal, an innovative Godunov finite-volume numerical scheme is proposed to suppress the spurious numerical oscillations occurring during rapid pipe pressurization. To dissipate the spurious numerical oscillations, we admit artificial numerical viscosity to the numerical scheme through applying a proposed Harten, Lax, and van Leer (HLL) Riemann solver for calculating the numerical fluxes at the computational cell interfaces. The proposed solver controls the magnitude of the numerical viscosity through adjusting the left and right wave velocities. A wave velocity calculator is proposed to optimally distribute the numerical viscosity over several computational cells around the computational cell in which the pressurization front is located. The proposed solver admits significant artificial numerical viscosity when the pipe pressurization is imminent and automatically reduces it in other places; in this way the numerical diffusion and data smearing is minimized. The validity of the proposed model is justified by the aid of several test cases in which the numerical results are compared with both experimental data and the results obtained from analytical methods. The results reveal that the proposed model succeeds in completely removing the spurious numerical oscillations, even when the pipe acoustic speed is over 1000 m/s. The numerical results also show that the model can successfully capture occurrence of negative pressures during the course of transient flow.

A new form of the Saint-Venant equations for variable topography

The solution stability of river models using the one-dimensional (1D) Saint-Venant equations can be easily undermined when source terms in the discrete equations do not satisfy the Lipschitz smoothness condition for partial differential equations. Although instability issues have been previously noted, they are typically treated as model implementation issues rather than as underlying problems associated with the form of the governing equations. This study proposes a new reference slope form of the Saint-Venant equations to ensure smooth slope source terms and eliminate one source of potential numerical oscillations. It is shown that a simple algebraic transformation of channel geometry provides a smooth reference slope while preserving the correct cross-section flow area and the total Piezometric pressure gradient that drives the flow. The reference slope method ensures the slope source term in the governing equations is Lipschitz continuous while maintaining all the underlying complexity of the real-world geometry. The validity of the mathematical concept is demonstrated with the open-source Simulation Program for River Networks (SPRNT) model in a series of artificial test cases and a simulation of a small urban creek. Validation comparisons are made with analytical solutions and the Hydrologic Engineering Center's River Analysis System (HEC-RAS) model. The new method reduces numerical oscillations and instabilities without requiring ad hoc smoothing algorithms.

Suppress Numerical Oscillations in Transient Mixed Flow Simulations with a Modified HLL Solver

Transition between free-surface and pressurized flows is a crucial phenomenon in many hydraulic systems. During simulation of such phenomenon, severe numerical oscillations may appear behind filling-bores, causing unphysical pressure variations and computation failure. This paper reviews existing oscillation-suppressing methods, while only one of them can obtain a stable result under a realistic acoustic wave speed. We derive a new oscillation-suppressing method with first-order accuracy. This simple method contains two parameters, Pa and Pb, and their values can be determined easily. It can sufficiently suppress numerical oscillations under an acoustic wave speed of 1000 ms−1. Good agreement is found between simulation results and analytical results or experimental data. This paper can help readers to choose an appropriate oscillation-suppressing method for numerical simulations of flow regime transition under a realistic acoustic wave speed.

A new form of the Saint–Venant equations for variable topography

The solution stability of river models using the one-dimensional (1D) Saint–Venant equations can be easily undermined when source terms in the discrete equations do not satisfy the Lipschitz smoothness condition for partial differential equations. Although instability issues have been previously noted, they are typically treated as model implementation issues rather than as underlying problems associated with the form of the governing equations. This study proposes a new reference slope form of the Saint–Venant equations to ensure smooth source terms and eliminate potential numerical oscillations. It is shown that a simple algebraic transformation of channel geometry provides a smooth reference slope while preserving the correct cross-sectional flow area and the total Piezometric pressure gradient that drives the flow. The reference slope method ensures the slope source term in the governing equations is Lipschitz-continuous while maintaining all the underlying complexity of the real-world geometry. The validity of the mathematical concept is demonstrated with the open-source SPRNT model in a series of artificial test cases and simulation of a small urban creek. Validation comparisons are made with analytical solutions and the HEC-RAS model. The new method reduces numerical oscillations and instabilities without requiring ad hoc smoothing algorithms.

Suppress Numerical Oscillations in Transient Mixed Flow Simulations with a Modified HLL Solver

Transition between free-surface and pressurized flows is an crucial phenomenon in many hydraulic systems, including water distribution systems, urban drainage systems, etc. During the transition, the force exerted on the structures changes drastically, thus it is meaningful to simulate this process. However, severe numerical oscillations are widely observed behind filling-bores, causing unphysical pressure variations and even computation failure. In this paper, some oscillation-suppressing approaches are reviewed and evaluated on a benchmark model. Then a new oscillation-suppressing approach is proposed to admit numerical viscosity when the water surface is at proximity of conduct roof which has first order accuracy. This approach adds numerical viscosity when water surface is at the proximity of conduct roof. It can sufficiently suppress numerical oscillations under an acoustic wave speed of 1000m/s and is simple to apply. In comparison with two experiments, the simulation results of this method show good agreement and little numerical oscillations. The results in this paper can help readers to choose an appropriate oscillation-suppressing method to improve the robustness and accuracy of flow regime transition simulations.

Finite point method of nonlinear convection diffusion equation

Aiming at the nonlinear convection diffusion equation with the numerical oscillations, a numerical stability algorithm is constructed. The basic principle of the finite point algorithm is given and the computational scheme of the nonlinear convection diffusion equation is deduced. Then, the numerical simulation of the one-dimensional and two-dimensional nonlinear convection-dominated diffusion equation is carried out. The relationship between the calculation result and the support domain size, step size and time is discussed. The results show that the algorithm has the characteristics of simplicity, stability and efficiency. Compared with the traditional finite element method and finite difference method, the new algorithm can attain a higher calculation accuracy. Simultaneously, it proves that the method given in this paper is effective to solve the nonlinear flow diffusion equation and can eliminate the numerical oscillations.

The incomplete reception error in acoustic analogy integral with source time domain algorithm

There are two algorithms to solve the retarded time equation in the acoustic analogy. One is the classic retarded time method, and the other is the source time domain algorithm or the advanced time approach. The latter is more effective and simple than the former. However, difficulties may arise in the reconstruction of the acoustic signal in the observer time domain. The signal interpolation in every observer time step and a completeness check at the end are necessary for the reconstruction. In addition, two error regions which cannot to be ignored in frequency domain are generated by the latter. They are called the incomplete reception error. It is the main purpose of present work to analyze the formation process and characteristics of the incomplete reception error. Then the analysis is tested with a simplified model and the numerical results show that there are some spurious numerical oscillations in frequency domain if the incomplete reception regions are not removed. Finally, the difference between the method of directly removing the incomplete reception regions and the standard acoustic signal post-processing method is compared. The comparison results show that the method of removing incomplete reception regions directly is better.