Modelling suspended sediment in environmental turbulent fluids

Cao, Meng; Roberts, A. J.

doi:10.1007/s10665-015-9817-7

Cited by 5 publications

(7 citation statements)

References 38 publications

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“…Direct numerical simulation of the complexities of turbulent floods over any reasonably large physical domain of interest is far too detailed to be yet feasible. However, we have previously derived shallow water models based upon the k ‐

ϵ

turbulence model, 40 and the Smagorinski model 41 . It is the latter that we choose as the highly nonlinear wave system to further test the staggered patch scheme.…”

Section: Nonlinear Turbulent Flood 2d Simulationmentioning

confidence: 99%

“…It is the latter that we choose as the highly nonlinear wave system to further test the staggered patch scheme. In terms of the depth h ( x , y , t ), and the depth‐averaged velocities

ū (x, y, t)

and

\overline{v} (x, y, t)

(with mean flow speed

\overline{q} = \sqrt{ū^{2} + {\overline{v}}^{2}}

) the example turbulent shallow water model pde s, 41 on a flat bed and with gravitational acceleration g , are

\begin{align} \frac{\partial h}{\partial t} prefix\approx & prefix- \frac{\partial}{\partial x} (h ū) prefix- \frac{\partial}{\partial y} (h \overset{v}{true}), \end{align}

\begin{align} \frac{\partial ū}{\partial t} prefix\approx & prefix- 0.00293 \frac{\overset{q}{true} ū}{h} prefix- 0.993 g \frac{\partial h}{\partial x} prefix- 1.045 ū \frac{\partial ū}{\partial x} prefix- 1.017 \overset{v}{true} \frac{\partial ū}{\partial y} + 0.094 \overset{q}{true} h \nabla^{2} ū, \end{align}

\begin{align} \frac{\partial \overset{v}{true}}{\partial t} prefix\approx & prefix- 0.00293 \frac{\overset{q}{true} \overset{v}{true}}{h} prefix- 0.993 g ∂<...> \end{align}

…”

Section: Nonlinear Turbulent Flood 2d Simulationmentioning

confidence: 99%

“…The detailed mathematical derivation of the pde s (15) generated more terms in its systematic asymptotic expansions 41 . However, neglecting terms with small coefficients that appear to have negligible effect on predictions, we arrive at the pde system (15).…”

Section: Nonlinear Turbulent Flood 2d Simulationmentioning

confidence: 99%

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Large‐scale simulation of shallow water waves via computation only on small staggered patches

Bunder

Divahar

Kevrekidis

et al. 2020

Numerical Methods in Fluids

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A multiscale computational scheme is developed to use given small microscale simulations of complicated physical wave processes to empower macroscale system‐level predictions. By coupling small patches of simulations over unsimulated space, large savings in computational time are realizable. Here, we generalize the patch scheme to the case of wave systems on staggered grids in two‐dimensional (2D) space. Classic macroscale interpolation provides a generic coupling between patches that achieves consistency between the emergent macroscale simulation and the underlying microscale dynamics. Spectral analysis indicates that the resultant scheme empowers feasible computation of large macroscale simulations of wave systems even with complicated underlying physics. As an example of the scheme's application, we use it to simulate some simple scenarios of a given turbulent shallow water model.

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ϵ

turbulence model, 40 and the Smagorinski model 41 . It is the latter that we choose as the highly nonlinear wave system to further test the staggered patch scheme.…”

Section: Nonlinear Turbulent Flood 2d Simulationmentioning

confidence: 99%

“…It is the latter that we choose as the highly nonlinear wave system to further test the staggered patch scheme. In terms of the depth h ( x , y , t ), and the depth‐averaged velocities

ū (x, y, t)

and

\overline{v} (x, y, t)

(with mean flow speed

\overline{q} = \sqrt{ū^{2} + {\overline{v}}^{2}}

) the example turbulent shallow water model pde s, 41 on a flat bed and with gravitational acceleration g , are

\begin{align} \frac{\partial h}{\partial t} prefix\approx & prefix- \frac{\partial}{\partial x} (h ū) prefix- \frac{\partial}{\partial y} (h \overset{v}{true}), \end{align}

\begin{align} \frac{\partial ū}{\partial t} prefix\approx & prefix- 0.00293 \frac{\overset{q}{true} ū}{h} prefix- 0.993 g \frac{\partial h}{\partial x} prefix- 1.045 ū \frac{\partial ū}{\partial x} prefix- 1.017 \overset{v}{true} \frac{\partial ū}{\partial y} + 0.094 \overset{q}{true} h \nabla^{2} ū, \end{align}

\begin{align} \frac{\partial \overset{v}{true}}{\partial t} prefix\approx & prefix- 0.00293 \frac{\overset{q}{true} \overset{v}{true}}{h} prefix- 0.993 g ∂<...> \end{align}

…”

Section: Nonlinear Turbulent Flood 2d Simulationmentioning

confidence: 99%

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Large‐scale simulation of shallow water waves via computation only on small staggered patches

Bunder

Divahar

Kevrekidis

et al. 2020

Numerical Methods in Fluids

View full text Add to dashboard Cite

show abstract

“…Direct numerical simulation of the complexities of turbulent floods over any reasonable physical domain of interest is far too detailed to be yet feasible. However, we have previously derived shallow water models based upon the Smagorinski (Cao & Roberts 2016a), and the k-turbulence models (Mei et al 2003). So in this section we take a step towards direct numerical simulation in patches by applying the patch scheme to the nonlinear, Smagorinski-based, shallow water model.…”

Section: Nonlinear Turbulent Flood 2d Simulationmentioning

confidence: 99%

“…Starting with the Smagorinski turbulence closure for 3D turbulent fluid flow (e.g., Ozgokmen et al 2007), Cao & Roberts (2016a) used centre manifold theory (e.g., Roberts 1988, Potzsche & Rasmussen 2006 to justify and construct a 'shallow water' model in terms of depth averaged velocities: we emphasise that these are not "depth averaged equations" but are the result of a systematic centre manifold modelling which is written in terms of "depth averaged quantities". In terms of the depth h(x, y, t), and the depth-averaged velocities ū(x, y, t) and v(x, y, t) (with mean flow speed q = √ ū2 + v2 ) the derived pdes are…”

Section: Model Turbulent Floods Via a Smagorinski Closurementioning

confidence: 99%

Large-scale simulation of shallow water waves with computation only on small staggered patches

Bunder¹,

Divahar²,

Kevrekidis³

et al. 2019

Preprint

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The multiscale patch scheme is built from given small micro-scale simulations of complicated physical processes to empower large macroscale simulations. By coupling small patches of simulations over unsimulated spatial gaps, large savings in computational time are possible. Here we discuss generalising the patch scheme to the case of wave systems on staggered grids in 2D space. Classic macro-scale interpolation provides a generic coupling between patches that achieves arbitrarily high order consistency between the emergent macro-scale simulation and the underlying micro-scale dynamics. Eigen-analysis indicates that the resultant scheme empowers feasible computation of large macro-scale simulations of wave systems even with complicated underlying physics. As examples we use the scheme to simulate some wave scenarios via a turbulent shallow water model.

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