An exact Riemann solver and a Godunov scheme for simulating highly transient mixed flows

Kerger, François; Archambeau, Pierre; Erpicum, Sébastien; Dewals, Benjamin; Pirotton, Michel

doi:10.1016/j.cam.2010.09.026

Cited by 59 publications

(54 citation statements)

References 16 publications

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“…In practice, the slot width T s is a parameter chosen to set the value of pressure wave speed a, which may range from 20-1250 m/s [37] depending on practical context and numerical constraints. In each pipe, the governing equations for A and Q are the de St. Venant equations for free-surface flow [16,23], where L is the length of the pipe, T is the duration of the study period, and…”

Section: Model the Preissman Slot Formulationmentioning

confidence: 99%

“…Initial conditions q(x, 0) are assumed to be known, and boundary conditions q(0, t) and q(L, t) are assigned based on the network connectivity and external inputs described in Section 3.2. The Preissman slot approach has been used, for example, by Trajkovic et al [32], who compared the model with experimental data; by Kerger et al [16], who implemented an exact Riemann solver and introduced a "negative slot" modification to handle subatmospheric pressure; by León et al, [22], who allowed the pressure wave speed to vary slightly; and by Borsche and Klar [1], who used a hexagonal cross-section to simplify the area-height relationship. Other transient flow models for air and water in single pipes include a "two-component pressure" approach [37,34]; a single-equation model with a modified pressure term [3,4]; a two-component model [23]; and a three-phase model accounting for air, air-water mixture, and water [15].…”

Section: Model the Preissman Slot Formulationmentioning

confidence: 99%

“…We used the same strategy to better approximate the quantity φ(A), which shows up in the speed estimation for the HLL solver and cannot be analytically expressed in terms of A. Several other authors use a ninth order McLaurin series for expressing φ as a function of θ [21,16], which avoids repeated quadrature but still relies on root finding for θ in terms of A. Furthermore, this expression also loses accuracy at the right end of the interval, with errors of order 10 −2 near the pipe crown.…”

Section: Reduction Of Variation In Pressurementioning

confidence: 99%

See 2 more Smart Citations

Optimizing Intermittent Water Supply in Urban Pipe Distribution Networks

Lieb¹,

Rycroft²,

Wilkening³

2016

SIAM J. Appl. Math.

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Abstract. In many urban areas of the developing world, piped water is supplied only intermittently, as valves direct water to different parts of the water distribution system at different times. The flow is transient, and may transition between free-surface and pressurized, resulting in complex dynamical features with important consequences for water suppliers and users. Here, we develop a computational model of transition, transient pipe flow in a network, accounting for a wide variety of realistic boundary conditions. We validate the model against several published data sets, and demonstrate its use on a real pipe network. The model is extended to consider several optimization problems motivated by realistic scenarios. We demonstrate how to infer water flow in a small pipe network from a single pressure sensor, and show how to control water inflow to minimize damaging pressure transients.1. Introduction. From the dry taps of Mumbai to the dusty reservoirs of São Paolo, urban water scarcity is a common condition of the present, and a likely feature of the future. Hundreds of millions of people worldwide are connected to water distribution systems subject to intermittency. This intermittent water supply may take many forms, from unexpected disruptions to planned supply cycles where pipes are filled and emptied regularly to shift water between different parts of the network at different times [17,33]. In Mumbai, for example, Vaivaramoorthy [33] reports that on average, residents have water flowing from their taps less than 8 out of 24 hours. Intermittent supply is often inequitable, with low-income neighborhoods experiencing lower water pressure and shorter supply durations than high-income ones [31]. Intermittent supply not only limits water availability, but also compromises water quality and damages infrastructure. With field data from urban India, Kumpel and Nelson [18] quantified the deleterious effect of intermittency on water quality, showing that both the initial flushing of water through empty pipes-as well as periods of low pressure-corresponded with periods of increased turbidity and bacterial contamination. Christodoulou [7] observed when that a drought in Cypress ushered in two years of intermittent supply, pipe ruptures increased by 30%-70% per year.Whereas intermittent water supply creates challenges for water managers and water users, the phenomenon creates opportunities for applied mathematics. It is an interesting and difficult mathematical problem to efficiently model transient pipe flow in networks-including transitions to and from pressurized states-with uncertain or complex boundary conditions. In this work we introduce a framework to not only describe intermittent water supply, but also use optimization to improve either our description of the system, or the operation of the described system in order to reduce risks such as infrastructure damage.Intermittent supply falls in somewhat of a modeling gap. Water distribution software abounds, including the free and open source software EPANET ...

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Section: Model the Preissman Slot Formulationmentioning

confidence: 99%

Section: Model the Preissman Slot Formulationmentioning

confidence: 99%

Section: Reduction Of Variation In Pressurementioning

confidence: 99%

See 1 more Smart Citation

Optimizing Intermittent Water Supply in Urban Pipe Distribution Networks

Lieb¹,

Rycroft²,

Wilkening³

2016

SIAM J. Appl. Math.

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show abstract

“…This observation indicates that numerical shock-capturing methods are partly inefficient in the presence of highly variable celerities, a shortcoming linked to the discretization of both the equations and the computational domain ). Kerger (2010) and Kerger et al (2011a) proved that any numerical shock-capturing solver is affected by this flaw.…”

Section: Air-entrapment: Moving Mixed Flowsmentioning

confidence: 99%

Three-phase bi-layer model for simulating mixed flows

Kerger

Archambeau

Dewals

et al. 2012

Journal of Hydraulic Research

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“…On the other hand, conventional numerical schemes need continuous solutions (i.e., finite difference method) and most of them were not designed to capture contact discontinuities, for instance, compressive or rarefaction shock. In previous works, the Godunov scheme has been recently applied to analyze transient twophase flow in rectangular and circular pipes for different research purposes (Kerger et al 2011;Bousso and Fuamba 2013). However, Godunov scheme is a useful numerical tool for dealing with free-surface gravity flow, compressible flow or multiphase flow.…”

Section: Introductionmentioning

confidence: 99%

Dynamic modeling of managed pressure drilling applying transient Godunov scheme

Sanchez-Barra

Nicolás-López

Valdiviezo-Mijangos

et al. 2015

J Petrol Explor Prod Technol

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Transient hydraulics always characterizes the circulating flow during managed pressure drilling. Therefore, the application of the Godunov scheme to oil-well drilling hydraulics is presented. The numerical model developed describes the treatment process of the initial and boundary conditions from the well geometry and true operational conditions. The well-known finite-volume method and Riemann problem are utilized for building the set of discrete equations. The account of Godunov's simulation describes the profiles of transient pressure and transient flow rate along the well. For attending the oil-field engineering concerns, the drilling parameters discussed are as follows: choke pressure, pumping pressure, bottom-hole pressure, and circulating flow rate. After the comparison between computed and well data, the results show a small difference of less than 7 and 1 % for pumping and bottomhole pressures, respectively. The main engineering contribution of this work is the solution and application of the first-order Godunov scheme to analyze the transient hydraulics during actual oil-well drilling and also the analysis and interpretation of the pressure wave behavior traveling along the well. The Godunov scheme has high-potential engineering applications for modeling the transient drilling hydraulics, i.e., controlled flow, underbalanced drilling, and foam cementing, as well.

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An exact Riemann solver and a Godunov scheme for simulating highly transient mixed flows

Cited by 59 publications

References 16 publications

Optimizing Intermittent Water Supply in Urban Pipe Distribution Networks

Optimizing Intermittent Water Supply in Urban Pipe Distribution Networks

Three-phase bi-layer model for simulating mixed flows

Dynamic modeling of managed pressure drilling applying transient Godunov scheme

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