scholarly journals Testing linear solvers for global gradient algorithm

2014 ◽  
Vol 16 (5) ◽  
pp. 1178-1193 ◽  
Author(s):  
Orazio Giustolisi ◽  
Naser Moosavian
Keyword(s):  
Linear System ◽  
Water Distribution ◽  
Direct Method ◽  
Mathematical Problem ◽  
Network Models ◽  
Water Distribution Network ◽  
Mass Conservation ◽  
Gradient Algorithm ◽  
Global Gradient Algorithm ◽  
Pressure Driven

Steady-state Water Distribution Network models compute pipe flows and nodal heads for assumed nodal demands, pipe hydraulic resistances, etc. The nonlinear mathematical problem is based on energy and mass conservation laws which is solved by using global linearization techniques, such as global gradient algorithm (GGA). The matrix of coefficients of the linear system inside GGA belongs to the class of sparse, symmetric and positive definite. Therefore a fast solver for the linear system is important in order to achieve the computational efficiency, especially when multiple runs are required. This work aims at testing three main strategies for the solution of linear systems inside GGA. The tests are performed on eight real networks by sampling nodal demands, considering the pressure-driven and demand-driven modelling to evaluate the robustness of solvers. The results show that there exists a robust specialized direct method which is superior to all the other alternatives. Furthermore, it is found that the number of times the linear system is solved inside the GGA does not depend on the specific solver, if a small regularization to the linear problem is applied, and that pressure-driven modelling requires a greater number which depends on the size and topology of the network and not only on the level of pressure deficiency.

scholarly journals Equivalent hydraulic resistance to simulate pipes subject to diffuse outflows

2011 ◽  
Vol 14 (1) ◽  
pp. 65-74 ◽  
Author(s):  
M. Ferrante ◽  
E. Todini ◽  
C. Massari ◽  
B. Brunone ◽  
S. Meniconi
Keyword(s):  
Hydraulic Resistance ◽  
Distribution System ◽  
Water Distribution ◽  
Water Distribution System ◽  
Distribution Network ◽  
Network Models ◽  
Water Distribution Network ◽  
Simulation Models ◽  
Gradient Algorithm ◽  
Present Generation

In water distribution network simulation models, pipes subject to diffuse outflow, either due to connections or to distributed demand or to leaks along their length, are generally converted into pipe elements only subject to lumped demand at their ending nodes. This approximation, which disregards the flow variation along the pipes, generates a loss of axial momentum, which is not correctly taken into account in the present generation of water distribution network models. In this paper a correction to the lumped demand approximation is provided and this equivalence is analyzed within the framework of the Global Gradient Algorithm. This is obtained through a correction of the pipe hydraulic resistance; this approach has proven to be more effective than the use of an asymmetrical lumped demand of the total distributed outflow at the pipe ending nodes. In order to assess the effect of the introduced correction, an application to a simple water distribution system is finally provided.

scholarly journals Limitations of demand- and pressure-driven modeling for large deficient networks

2017 ◽  
Vol 10 (2) ◽  
pp. 93-98 ◽  
Author(s):  
Mathias Braun ◽  
Olivier Piller ◽  
Jochen Deuerlein ◽  
Iraj Mortazavi
Keyword(s):  
Water Distribution ◽  
Network Models ◽  
Distribution Networks ◽  
Computer Applications ◽  
State Variables ◽  
Modeling Process ◽  
Uniqueness Of The Solution ◽  
Basic Equations ◽  
Physical Phenomena ◽  
Pressure Driven

Abstract. The calculation of hydraulic state variables for a network is an important task in managing the distribution of potable water. Over the years the mathematical modeling process has been improved by numerous researchers for utilization in new computer applications and the more realistic modeling of water distribution networks. But, in spite of these continuous advances, there are still a number of physical phenomena that may not be tackled correctly by current models. This paper will take a closer look at the two modeling paradigms given by demand- and pressure-driven modeling. The basic equations are introduced and parallels are drawn with the optimization formulations from electrical engineering. These formulations guarantee the existence and uniqueness of the solution. One of the central questions of the French and German research project ResiWater is the investigation of the network resilience in the case of extreme events or disasters. Under such extraordinary conditions where models are pushed beyond their limits, we talk about deficient network models. Examples of deficient networks are given by highly regulated flow, leakage or pipe bursts and cases where pressure falls below the vapor pressure of water. These examples will be presented and analyzed on the solvability and physical correctness of the solution with respect to demand- and pressure-driven models.

scholarly journals Experimental investigation of leak hydraulics

2012 ◽  
Vol 15 (3) ◽  
pp. 666-675 ◽  
Author(s):  
M. Ferrante ◽  
C. Massari ◽  
E. Todini ◽  
B. Brunone ◽  
S. Meniconi
Keyword(s):  
Distribution Systems ◽  
Water Distribution ◽  
Network Models ◽  
Water Distribution Network ◽  
Experimental Tests ◽  
Pressure Control ◽  
Pipe Material ◽  
Governing Equations ◽  
The One ◽  
Definition Of

In recent decades the hydraulics of leaks, i.e. the definition of the relationships linking the hydraulic quantities in pipes with leaks, has received increasing attention. On the one hand, the definition of the relationship between the leak outflow and the relevant parameters – e.g. the leak area and shape, the pressure inside the pipe and outside the leak, and the pipe material – is crucial for pressure control and inverse analysis techniques. On the other hand, if the effect of the leakage on the governing equations is not taken into account, i.e. the loss of the flow axial momentum is not considered, significant errors can be introduced in the simulation of water distribution systems. In this paper, the governing equations for a pipe with a leak are derived. The basic equations, obtained within different approaches, are presented in a consistent formulation and then compared with the results of some experimental tests. The leak jet angle and other major features of the results are analysed. The estimated values of the parameters can be used in the water distribution network models when pipes with a diffuse leakage are considered.

Uncertainty quantification of pressure-driven analysis for water distribution network modeling

2015 ◽  
Vol 16 (3) ◽  
pp. 599-610 ◽  
Author(s):  
Ho Min Lee ◽  
Do Guen Yoo ◽  
Doosun Kang ◽  
Hwandon Jun ◽  
Joong Hoon Kim
Keyword(s):  
Negative Pressure ◽  
Water Distribution ◽  
Real Life ◽  
Water Distribution Network ◽  
Distribution Networks ◽  
Operating Conditions ◽  
Service Reliability ◽  
High Degree ◽  
Pressure Driven Analysis ◽  
Pressure Driven

The hydraulic analysis of water distribution networks (WDNs) is divided into two approaches: namely, a demand-driven analysis (DDA) and a pressure-driven analysis (PDA). In the DDA, the basic assumption is that the nodal demand is fully supplied irrespective of the nodal pressure, which is mainly suitable for normal operating conditions. However, in abnormal conditions, such as pipe failures or unexpected increase in demand, the DDA approach may cause unrealistic results, such as negative pressure. To address the shortcomings of DDA, PDA has been considered in a number of studies. For PDA, however, the head-outflow relation (HOR) should be given, which is known to contain a high degree of uncertainty. Here, the DDA-based simulator, EPANET2 was modified to develop a PDA model simulating pressure deficient conditions and a Monte Carlo simulation (MCS) was performed to consider the quantitative uncertainty in HOR. The developed PDA model was applied to two networks (a well-known benchmark system and a real-life WDN) and the results showed that the proposed model is superior to other reported models when dealing with negative pressure under abnormal conditions. In addition, the MCS-based sensitivity analysis presents the ranges of pressure and available discharge, quantifying service reliability of water networks.

scholarly journals Limitations of Demand- and Pressure-Driven Modeling for Large Deficient Networks

2017 ◽  
Author(s):  
Mathias Braun ◽  
Olivier Piller ◽  
Jochen Deuerlein ◽  
Iraj Mortazavi
Keyword(s):  
Water Distribution ◽  
Network Models ◽  
Distribution Networks ◽  
Computer Applications ◽  
State Variables ◽  
Modeling Process ◽  
Uniqueness Of The Solution ◽  
Basic Equations ◽  
Physical Phenomena ◽  
Pressure Driven

Abstract. The calculation of hydraulic state variables for a network is an important task in managing the distribution of potable water. Over the years the mathematical modeling process has been improved by numerous researchers for the utilization in new computer applications and the more realistic modeling of water distribution networks. But, in spite of these continuous advances, there are still a number of physical phenomena that cannot be tackled correctly by current models. This paper will take a closer look on the two modeling paradigms given by demand and pressure driven modeling. The basic equations are introduced and parallels are drawn to the optimization formulations from electrical engineering. These formulations guarantee existence and uniqueness of the solution. One of the central questions in the French and German research project ResiWater is the investigation of the network resilience in case of extreme events or disasters. Under such extraordinary conditions where models are pushed beyond their limits we talk of deficient network models. Examples of deficient networks are given by highly regulated flow, leakage or pipe bursts and cases where pressure falls below the vapor-pressure of water. These examples will be presented and analyzed on the solvability and physical correctness of the solution with respect to demand and pressure driven models.

scholarly journals Online simplification of water distribution network models for optimal scheduling

2013 ◽  
Vol 15 (3) ◽  
pp. 652-665 ◽  
Author(s):  
Daniel Paluszczyszyn ◽  
Piotr Skworcow ◽  
Bogumil Ulanicki
Keyword(s):  
Distribution Systems ◽  
Water Distribution ◽  
Distribution Network ◽  
Network Models ◽  
Water Distribution Network ◽  
Simplified Model ◽  
Reduced Model ◽  
Water Network ◽  
Pump Speed ◽  
Online Optimisation

This paper presents an implementation of an extended simplification algorithm of water distribution network models for the purpose of inclusion in the online optimisation strategy for energy and leakage management in water distribution systems. Whereas the previously proposed reduced model represented accurately the original hydraulic water network characteristics, the energy distribution in the simplified model was not preserved. This could cause a situation where the pump speed required to satisfy specified minimum pressure constraints is different for the reduced model and the original model. This problem has been identified, and an appropriate modification to the simplification algorithm has been introduced. The idea comprises introduction of the energy audit of the water network and the calculation of new minimum service pressure constraints for the simplified model. The approach allows the preservation of both hydraulic and energetic characteristics of the original water network and therefore meets the requirements of the online optimisation strategy. Suitability of the proposed approach is evaluated via a case study. The modern parallel programming implementation allowed water network models consisting of several thousand elements to be reduced within 2 min with an average relative accuracy of less than 2% in terms of tanks flows.

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