2D Modeling of Flow and Sediment Interaction: Sediment Mixtures

Budinski, Ljubomir; Spasojevic, Miodrag

doi:10.1061/(asce)ww.1943-5460.0000226

Cited by 11 publications

(14 citation statements)

References 18 publications

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“…The developed numerical model incorporates the depth‐averaged flow equations in the orthogonal curvilinear coordinate system (Hsieh and Yang, ; Hsieh and Yang, ; Budinski and Spasojević, ; Horvat et al, ) that were solved using the principles outlined in the fractional‐step method (Yanenko, ). Applying this method resulted in three subsequent steps for water flow computation; these are the advection step

\begin{matrix} center \\ center {(\frac{\partial u}{\partial t})}^{a} = - \frac{u}{h_{ξ}} \frac{\partial u}{\partial ξ} - \frac{v}{h_{η}} \frac{\partial u}{\partial η} - \frac{1}{h_{ξ} h_{η}} \frac{\partial h_{ξ}}{\partial η} v u + \frac{1}{h_{ξ} h_{η}} \frac{\partial h_{η}}{\partial ξ} v^{2} \\ center {(\frac{\partial v}{\partial t})}^{a} = - \frac{u}{h_{ξ}} \frac{\partial v}{\partial ξ} - \frac{v}{h_{η}} \frac{\partial v}{\partial η} - \frac{1}{h_{η} h_{ξ}} \frac{\partial h_{η}}{\partial ξ} u v + \frac{1}{h_{η} h_{ξ}} \frac{\partial h_{ξ}}{\partial η} u^{2} \end{matrix}

and the diffusion step

\begin{matrix} center \\ center {(\frac{\partial u}{\partial t})}^{a + d} - {(\frac{\partial u}{\partial t})}^{a} & center = \frac{1}{h_{ξ} h_{η} d} [\frac{\partial}{\partial ξ} (2 <...>) \end{matrix}

…”

Section: Numerical Modelmentioning

confidence: 99%

“…The adsorbed pollutant source term that accounts for the sediment entrainment/deposition (Budinski and Spasojević, ; Horvat et al, ) is, quite naturally, determined using the appropriate sediment processes

S_{k}^{‡} = E_{k}^{normals normale normald} β_{k}^{‡} - D_{k}^{normals normale normald} β_{k}^{‡}

…”

Section: Numerical Modelmentioning

confidence: 99%

“…The developed numerical model incorporates the depthaveraged flow equations in the orthogonal curvilinear coordinate system (Hsieh and Yang, 2003;Hsieh and Yang, 2004;Budinski and Spasojević, 2013;Horvat et al, 2015) that were solved using the principles outlined in the fractional-step method (Yanenko, 1971). Applying this method resulted in three subsequent steps for water flow computation; these are the advection step ∂u ∂t…”

Section: Water Flow Modelmentioning

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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\begin{matrix} center \\ center {(\frac{\partial u}{\partial t})}^{a} = - \frac{u}{h_{ξ}} \frac{\partial u}{\partial ξ} - \frac{v}{h_{η}} \frac{\partial u}{\partial η} - \frac{1}{h_{ξ} h_{η}} \frac{\partial h_{ξ}}{\partial η} v u + \frac{1}{h_{ξ} h_{η}} \frac{\partial h_{η}}{\partial ξ} v^{2} \\ center {(\frac{\partial v}{\partial t})}^{a} = - \frac{u}{h_{ξ}} \frac{\partial v}{\partial ξ} - \frac{v}{h_{η}} \frac{\partial v}{\partial η} - \frac{1}{h_{η} h_{ξ}} \frac{\partial h_{η}}{\partial ξ} u v + \frac{1}{h_{η} h_{ξ}} \frac{\partial h_{ξ}}{\partial η} u^{2} \end{matrix}

and the diffusion step

\begin{matrix} center \\ center {(\frac{\partial u}{\partial t})}^{a + d} - {(\frac{\partial u}{\partial t})}^{a} & center = \frac{1}{h_{ξ} h_{η} d} [\frac{\partial}{\partial ξ} (2 <...>) \end{matrix}

…”

Section: Numerical Modelmentioning

confidence: 99%

S_{k}^{‡} = E_{k}^{normals normale normald} β_{k}^{‡} - D_{k}^{normals normale normald} β_{k}^{‡}

…”

Section: Numerical Modelmentioning

confidence: 99%

Section: Water Flow Modelmentioning

confidence: 99%

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Two Dimensional Heavy Metal Transport Model for Natural Watercourses

Horvat

2015

River Res. Applic.

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“…У скорије време се у хидрауличкој пракси редовно користе равански модели [1]. Наводе се једначине струјања у картезијанском координатном систему [2]     …”

Section: уводunclassified

Granični Uslovi Za Hidraulički Proračun Kod Ravanskih Modela

Horvat¹,

Horvat²

2014

Zbornik GFS

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“…The second computer code is the Telemac-2D, which also makes use of the fractional step method, but relies on the finite element approach, based on an unstructured computational mesh [2]. Even though different authors [3] have developed accurate methods for wetting and drying, grid-based solvers are restricted in cases of rapidly changing flows. On the contrary, methods relying on particle tracking are very adjustable in this respect [4].…”

Section: Introductionmentioning

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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2D Modeling of Flow and Sediment Interaction: Sediment Mixtures

Cited by 11 publications

References 18 publications

Two Dimensional Heavy Metal Transport Model for Natural Watercourses

Two Dimensional Heavy Metal Transport Model for Natural Watercourses

Granični Uslovi Za Hidraulički Proračun Kod Ravanskih Modela

Different approaches to two-dimensional numerical modelling of natural watercourses

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