Advection step in the split-operator approach applied to river modeling

Isić, Mirjana; Horvat, Zoltan; Spasojevic, Miodrag

doi:10.1016/j.apnum.2013.05.001

Cited by 6 publications

(9 citation statements)

References 30 publications

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“…Therefore, the computational procedures used to solve Equations 1, 2 and 3 are only given in a form of a short summary. Because the advection step equations have a hyperbolic character, they can be solved with the characteristic method using the principles given by Benqué et al (1982), Holly and Usseglio-Polatera (1984) and Isic et al (2013). Partial differential equations 1 are transformed into ordinary differential equations along the characteristic curves.…”

Section: Water Flow Modelmentioning

confidence: 99%

“…This section presents the developed heavy metal transport model that is formulated in accordance with the activelayer concept (Budinski and Spasojević, 2013) and the split-operator approach (Yanenko, 1971;Isic et al, 2013;Horvat et al, 2015). Heavy metals in natural watercourses can be classified as non conservative pollutants, which have a certain tendency to be fixed to sediment particles.…”

Section: Metal Transport Modelmentioning

confidence: 99%

“…Using multiple schematic examples, the authors were able to derive conclusions with respect to the models' numerical stability by altering different computational parameters until generating the breakdown of the solution, conservation errors by analysing the mass conservation equations and performing grid convergence tests that resulted in rates of convergence varying from 1.01 to 1.48 for different variables and so on. Considering that the equations used for heavy metal and sediment transport have the same mathematical character as well as the same structure, conducting tests regarding numerical stability, conservation error analysis and grid convergence would essentially boil down to reproducing previously conducted tests published as a part of the flow and sediment transport model study (Isic et al, 2013;Horvat et al, 2015). Consequently, these tests are omitted, and the developed two-dimensional heavy metal transport model was implemented using field measurements.…”

Section: Model Applicationmentioning

confidence: 99%

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Two Dimensional Heavy Metal Transport Model for Natural Watercourses

Horvat

2015

River Res. Applic.

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This work presents the development and calibration of a two-dimensional (depth-averaged) river flow, sediment transport and heavy metal transport model in natural watercourses. Because heavy metals occur in dissolved and adsorbed phases, implementing the active-layer concept for sediment transport computation enabled the development of a heavy metal transport model that accounts for pollutant moving in dissolved phase, adsorbed on suspended sediment, adsorbed on bed-load, deposited in the active-layer of the river bed or adsorbed on sediment in deeper strata. The proposed concept also enables the modelling of pollutant exchange processes using accessible sediment particle surface area for suspended and bed sediment separately. The presented heavy metal transport model is able to manage sediment mixtures found in natural watercourses using an arbitrary number of sediment size-classes, distinguishing in this way smaller size-classes that engage in interaction with the pollutant. Using field measurements for a reach of the Danube River, simulations were conducted for water flow, sediment transport and heavy metal transport. While some discrepancies between measured and computed values for pollutant concentrations were observed, the model reproduced the water and sediment contamination quite reasonably with acceptable mass conservation errors. The simulations also gave an insight in the general behaviour of the monitored heavy metals in the considered river reach. Therefore, it can be concluded that the developed model is suitable for simulating complex flow, sediment transport and heavy metal transport conditions in natural watercourses.

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Section: Water Flow Modelmentioning

confidence: 99%

Section: Metal Transport Modelmentioning

confidence: 99%

Section: Model Applicationmentioning

confidence: 99%

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Two Dimensional Heavy Metal Transport Model for Natural Watercourses

Horvat

2015

River Res. Applic.

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“…Предметне једначине су решаване применом методе етапног решавања (разломљених корака), па се оне растављају на три сукцесивна корака: адвективни, дифузиони и пропагациони. Пошто адвективни корак има изразито хиперболички карактер, он се решава методом карактеристика [4]. У случају дифузионог и пропагационог корака се користи метода коначних разлика у комбинацији са АДИ методом [1] и Томасовим алгоритмом.…”

Section: модел течења водеunclassified

Princip Modelisanja Transporta Zagađivača U Prirodnim Vodotocima

Horvat¹,

Horvat²,

Hovanj³

2015

Zbornik GFS

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This work presents the principles of two-dimensional modeling of pollutant transport in natural watercourses. The model incorporates water flow computation, both aspects of sediment transport (suspended and bed-load), as well as the processes of nonconservative pollutant transport including its interaction with sediment particles by adsorption/desorption. Deriving the governing equations for pollutant transport included the dissolved and adsorbed pollutant. The exchange between the dissolved and adsorbed pollutant was described using a first order kinetic process, while the modeling of the exchange coefficients remained closely related to the sediment surface available for adsorption.

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“…Similar to Telemac-2D, the integration along characteristic curves is accomplished by dividing them into an arbitrary number of straight sub-segments [1]. The resulting equations for velocity components are nonlinear, and are solved using the NewtonRaphson iterative algorithm [16][17][18]. The diffusion step equations: (7) are discretized using finite differences with the Crank-Nicolson time-integration scheme [19].…”

Section: Mobed2 Codementioning

confidence: 99%

Different approaches to two-dimensional numerical modelling of natural watercourses

2018

JCE

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Different approaches to two-dimensional numerical modelling of natural watercoursesResults obtained by analysis of three different approaches to numerical modelling of open watercourses are presented in the paper. Two examples of flow, uniform flow on the physical model of a curve at the Tisza River and nonuniform flow at the Danube River, are analysed. Standard error analysis has revealed that results of the similar order of magnitude are obtained in implementation of two numerical methods in which computational grids are used, while the method in which computational grid is not used, i.e. the smoothed particle hydrodynamics method, requires further improvements to enable successful modelling of the gradually variable flow. Key words:2D flow, finite element method, finite difference method, smoothed particle hydrodynamics method Pregledni rad Zoltan Horvat, Mirjana Horvat, Nikola Rosić, Budo Zindović, Radomir Kapor Različiti pristupi dvodimenzionalnom numeričkom modeliranju prirodnih vodotoka U radu su prikazani rezultati analize tri različita pristupa numeričkom modeliranju otvorenih vodotoka. Analizirana su dva primjera strujanja, jednoliko strujanje na fizikalnom modelu krivine na rijeci Tisi i nejednoliko strujanje na rijeci Dunavu. Analiza standardne pogreške pokazala je da se upotrebom dviju numeričkih metoda u kojima se koriste računske mreže dobivaju rezultati istog reda točnosti, dok metoda u kojoj se ne koristi računska mreža, metoda hidrodinamike izglađenih čestica, zahtijeva daljnja poboljšanja kako bi se uspješno modeliralo postupno promjenjivo strujanje.

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Advection step in the split-operator approach applied to river modeling

Cited by 6 publications

References 30 publications

Two Dimensional Heavy Metal Transport Model for Natural Watercourses

Two Dimensional Heavy Metal Transport Model for Natural Watercourses

Princip Modelisanja Transporta Zagađivača U Prirodnim Vodotocima

Different approaches to two-dimensional numerical modelling of natural watercourses

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