scholarly journals Water quality model with axial dispersion solved by Eulerian-Lagrangian operator-splitting method in water distribution system

2017 ◽  
Vol 18 (3) ◽  
pp. 831-842 ◽  
Author(s):  
Guoqiang Chen ◽  
Tianyu Long ◽  
Yun Bai
Keyword(s):  
Water Quality ◽  
Distribution System ◽  
Water Distribution ◽  
Operator Splitting ◽  
Splitting Method ◽  
Axial Dispersion ◽  
Water Quality Simulation ◽  
Operator Splitting Method ◽  
Lagrangian Operator ◽  
Simulation Results

Abstract This study explores the effects of water quality simulation results by embedding axial dispersion into the classical advective-reactive model in a water distribution system. The Eulerian-Lagrangian operator-splitting method is employed to solve the model with axial dispersion. Satisfactory results were obtained after the numerical solution was tested against the analytical and other numerical solutions. The water quality simulation results without the reaction item show that when water velocity is low (or Peclet numbers are small), dispersion is dominant and significantly affects the numerical simulation results. The contaminant concentration at downstream node gradually increased with time along the upstream pipelines from the source, which is particularly reflected in the terminal. The simulation results show that the biomass concentration may demonstrate synthetic effects of axial dispersion and reaction, i.e. mutual promotion, given the multicomponent (substrate, residual chlorine, and microbial biomass) reaction-transport processes. It is particularly reflected in the low flow velocity.

scholarly journals Analytical Solutions to Conservative and Non-Conservative Water Quality Constituents in Water Distribution System Storage Tanks

Water ◽  
2021 ◽  
Vol 13 (24) ◽  
pp. 3502
Author(s):  
Biniam Abrha ◽  
Avi Ostfeld
Keyword(s):  
Water Quality ◽  
Distribution System ◽  
Distribution Systems ◽  
Water Distribution ◽  
Compartment Model ◽  
Storage Tanks ◽  
Water Quality Simulation ◽  
Negative Impacts ◽  
Critical Components

Water storage tanks are one of the primary and most critical components of water distribution systems (WDSs), which aim to manage water supply by maintaining pressure. In addition, storage provides a surplus source of water in case of an emergency. To gain the mentioned advantages, storage tanks are incorporated in most WDSs. Despite these advantages, storage can also pose negative impacts on water quality, thereby affecting water utilities. Water quality problems are a result of longer residency times and inadequate water mixing. This study aimed to construct a model of a tank’s water quantity and quality by formulating and solving governing equations based on inlet/outlet configurations and processes that influence the movement of water and chemical substances inside it. We used a compartment model to characterize the mixing behavior inside a tank. A water quality simulation model with different compartment arrangements was explored for extended filling and draining of storage, which was further validated using a previously published case study.

scholarly journals The Sum and Difference of Two Lognormal Random Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
C. F. Lo
Keyword(s):  
Stochastic Process ◽  
Probability Distributions ◽  
Operator Splitting ◽  
Splitting Method ◽  
Unified Approach ◽  
New Approach ◽  
Numerical Examples ◽  
Operator Splitting Method ◽  
Approximate Probability ◽  
Analytical Series

We have presented a new unified approach to model the dynamics of both the sum and difference of two correlated lognormal stochastic variables. By the Lie-Trotter operator splitting method, both the sum and difference are shown to follow a shifted lognormal stochastic process, and approximate probability distributions are determined in closed form. Illustrative numerical examples are presented to demonstrate the validity and accuracy of these approximate distributions. In terms of the approximate probability distributions, we have also obtained an analytical series expansion of the exact solutions, which can allow us to improve the approximation in a systematic manner. Moreover, we believe that this new approach can be extended to study both (1) the algebraic sum ofNlognormals, and (2) the sum and difference of other correlated stochastic processes, for example, two correlated CEV processes, two correlated CIR processes, and two correlated lognormal processes with mean-reversion.

scholarly journals DEVELOPMENT OF CLEAN WATER DISTRIBUTION NETWORK SYSTEM IN GENTENG SUB-DISTRICT BANYUWANGI USING EPANET 2.0 PROGRAM

2019 ◽  
Vol 3 (2) ◽  
pp. 172
Author(s):  
Ayu Rahmad Jayanti ◽  
Ririn Endah Badriani ◽  
Yeny Dhokhikah
Keyword(s):  
Discharge Capacity ◽  
Distribution System ◽  
Water Distribution ◽  
Water Discharge ◽  
Distribution Network ◽  
Water Distribution Network ◽  
Public Works ◽  
Network System ◽  
Clean Water ◽  
Simulation Results

The clean water distribution in the Genteng Subdistrict, Banyuwangi Regency is included in the service area of the Zone 1 PDAM tile unit. The 60 liters/second reservoir discharge capacity is obtained from Sumber Umbul Sari in the Glenmore District. The distribution of clean water in Zone 1 is still less than 70% of the area served, as the installed discharge capacity is estimated to be insufficient. In order to achieve the distribution goal, a network system must be developed by adding direct debits and planning a new pipeline. The Epanet 2.0 program simplifies the calculation of pipeline networks by integrating elevation data, network maps, pipeline specification, and load. The analysis of the simulation results was conducted using the Public Works Minister's hydraulic parameter standards 2007. Planning of a distribution network and a cost budget in 2029 were done to estimate the water supply needs and budgets required. The hydraulic simulation results based on the analysis of the pressure of all joints are in accordance with the standard, while the analysis of the velocity in pipe is less standard. The need for water discharge in 2029 is 71.6 liters/second. In Kembiritan Village, the construction of distribution pipes with an additional reservoir unit was planned. The planned pipe dimensions in the development area were 25 mm at 796 meters, 50 mm at 4062 meters, and 75 mm at 1518 meters. The cost of planning a clean water distribution system in 2029 is Rp. 1,431,375,000.00. Distribusi air bersih di Kecamatan Genteng Kabupaten Banyuwangi merupakan wilayah pelayanan Zona 1 PDAM unit Genteng. Kapasitas debit reservoir sebesar 60 liter/detik berasal dari sumber umbul sari di Kecamatan Glenmore. Pendistribusian air bersih di wilayah Zona 1 masih kurang dari 70% wilayah yang terlayani, karena diperkirakan kapasitas debit yang terpasang kurang mencukupi. Untuk memenuhi target pemerataan distribusi perlu pengembangan sistem jaringan dengan penambahan debit dan perencanaan jaringan pipa baru. Program Epanet 2.0 memudahkan dalam perhitungan jaringan perpipaan dengan mengintegrasi data elevasi, peta jaringan, spesifikasi pipa dan debit. Analisis hasil simulasi menggunakan standar parameter hidrolis Permen PU 2007. Perencanaan pengembangan jaringan distribusi dan anggaran biaya pada tahun 2029 guna memperkirakan debit kebutuhan air dan anggaran biaya yang dibutuhkan. Hasil simulasi hidrolis berdasarkan analisis tekanan semua junction telah sesuai standar, sedangkan analisis kecepatan masih di bawah standar. Kebutuhan debit air tahun 2029 sebesar 71,6 Liter/detik. Pengembangan pipa distribusi direncanakan di Desa Kembiritan dengan tambahan satu unit reservoir. Dimensi pipa rencana di wilayah pengembangan digunakan diameter 25 mm sepanjang 796 m, diameter 50 mm sepanjang 4062 m dan diameter 75 mm sepanjang 1518 m. Biaya perencanaan sistem distribusi air bersih tahun 2029 sebesar Rp. 1.431.375.000,00.

scholarly journals COSMO: A Conic Operator Splitting Method for Convex Conic Problems

2021 ◽  
Vol 190 (3) ◽  
pp. 779-810
Author(s):  
Michael Garstka ◽  
Mark Cannon ◽  
Paul Goulart
Keyword(s):  
Convex Sets ◽  
Operator Splitting ◽  
Splitting Method ◽  
Computational Cost ◽  
Coefficient Matrix ◽  
Benchmark Problems ◽  
Portfolio Optimisation ◽  
Splitting Algorithm ◽  
Semidefinite Programs ◽  
Operator Splitting Method

AbstractThis paper describes the conic operator splitting method (COSMO) solver, an operator splitting algorithm and associated software package for convex optimisation problems with quadratic objective function and conic constraints. At each step, the algorithm alternates between solving a quasi-definite linear system with a constant coefficient matrix and a projection onto convex sets. The low per-iteration computational cost makes the method particularly efficient for large problems, e.g. semidefinite programs that arise in portfolio optimisation, graph theory, and robust control. Moreover, the solver uses chordal decomposition techniques and a new clique merging algorithm to effectively exploit sparsity in large, structured semidefinite programs. Numerical comparisons with other state-of-the-art solvers for a variety of benchmark problems show the effectiveness of our approach. Our Julia implementation is open source, designed to be extended and customised by the user, and is integrated into the Julia optimisation ecosystem.

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