Extension and application of the Preissmann slot model to 2D transient mixed flows

Maranzoni, Andrea; Dazzi, Susanna; Aureli, Francesca; Mignosa, Paolo

doi:10.1016/j.advwatres.2015.04.010

Cited by 28 publications

(42 citation statements)

References 36 publications

(79 reference statements)

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“…The 2D extension of the classic Preissmann slot concept on a Cartesian grid is based on the idea that a top surface is defined for each computational cell, and 2 narrow vertical slots, parallel to the 2 plane Cartesian directions x and y , are added above (Figure ), thereby creating an ideal lattice of orthogonal slots over all the computational domain . For the single Cartesian element sketched in Figure , h and H denote the piezometric head and the ceiling elevation above the bottom, respectively, Δ x and Δ y are the cell sizes, while T y and T x are the widths of the slots along the x ‐axis and y ‐axis directions, respectively.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The mass and linear momentum principles applied to a fixed control volume for incompressible flow under the shallow water approximation lead to the following well‐known conservation form of the 2D governing equations [eg, ]:

\frac{\partial boldU}{\partial t} + \frac{\partial boldF}{\partial x} + \frac{\partial boldG}{\partial y} = boldS,

where U is the vector of the conserved variables, F and G are the flux vectors along the x and y directions, respectively, and S is the source term. For the Cartesian control element in Figure , these vectors read

boldU = ([], \begin{array}{c} center & \overset{h}{true} \\ center & {\overset{true¯}{q}}_{x} \\ center & {\overset{true¯}{q}}_{y} \end{array}), boldF = ([], \begin{array}{c} center & {\overset{true¯}{q}}_{x} \\ center & {\overset{true¯}{q}}_{x}^{2} true/ {\overset{true¯}{h}}_{x} + g ζ_{x} {\overset{true¯}{h}}_{x} \\ center & {\overset{true¯}{q}}_{x} {\overset{true¯}{q}}_{y} true/ {\overset{true¯}{h}}_{y} \end{array}), boldG = ([], \begin{array}{c} center & {\overset{true¯}{q}}_{y} \\ center & {\overset{true¯}{q}}_{x} {\overset{true¯}{q}}_{y} true/ {\overset{true¯}{h}}_{x} \\ center & {\overset{true¯}{q}}_{y}^{2} true/ {\overset{true¯}{h}}_{y} + g ζ_{y} {\overset{true¯}{h}}_{y} \end{array}), boldS = ([], \begin{array}{c} center & 0 \\ center & g {\overset{true¯}{h}}_{x} ((), S_{0 x} - S_{normalf x}) \\ center & g {\overset{true¯}{h}}_{y} ((), <...>) \end{array})

…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Maranzoni et al have shown that Equations to are strictly hyperbolic for h > 0 and reduce to the classic 2D SWE for free surface flows when 0 ≤ h ≤ H .…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The flow variables at cell boundaries are reconstructed by means of the MUSCL‐Hancock method by applying the Van Leer slope limiter function . For more details about the numerical algorithm, see Maranzoni et al, and Aureli et al…”

Section: Mathematical Modelmentioning

confidence: 99%

“…A typical case encountered in practice concerns the inlet and outlet of crossing structures located in flooding areas. The original method by Maranzoni et al is not actually completely effective in handling this type of singularities because the dynamic action of the structure deck on the flow is neglected. This paper aims to address this issue by proposing a numerical strategy inspired by the C ‐property satisfying scheme suggested by Zhou et al to deal with a bottom step discontinuity in the context of MUSCL‐Hancock SGM methods .…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Numerical treatment of a discontinuous top surface in 2D shallow water mixed flow modeling

Maranzoni

Mignosa

2017

Numerical Methods in Fluids

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Summary This paper presents a numerical strategy based on shallow water equations (SWE) coupled with the 2D Preissmann slot model to handle a ceiling step discontinuity in finite volume schemes for mixed flow modeling. In practice, a typical situation would be a closed structure, such as a bridge or culvert, which induces a sudden vertical flow constriction and may even run partly or totally full in high flow conditions. In such case, both the inlet and outlet of the structure involve a discontinuity in the top elevation. This special singularity is topologically represented by inserting a fictitious cell between 2 adjacent computational cells characterized by sharply different ceiling elevation. The 2D SWE are solved by means of a well‐balanced quasi‐conservative Godunov‐type numerical scheme based on the Slope Limiter Centered (SLIC) scheme. The flow variables at each boundary of the fictitious cell are reconstructed by adopting the cross‐sectional shape of the adjoining cell. Accordingly, the dynamic effect of the structure deck on the flow is suitably modeled, and the C‐property for a stationary solution is rigorously satisfied, even when the closed structure is partially full. The capability of the numerical scheme is verified by comparison with both novel analytical solutions of 1D Riemann problems with a ceiling step discontinuity and experimental data of steady and unsteady mixed flows available in literature. Finally, a real‐scale application to a multiple arch bridge is presented. The results show that the method is robust and effective in predicting the 2D features induced by a crossing structure on the flow dynamics.

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Section: Mathematical Modelmentioning

confidence: 99%

\frac{\partial boldU}{\partial t} + \frac{\partial boldF}{\partial x} + \frac{\partial boldG}{\partial y} = boldS,

boldU = ([], \begin{array}{c} center & \overset{h}{true} \\ center & {\overset{true¯}{q}}_{x} \\ center & {\overset{true¯}{q}}_{y} \end{array}), boldF = ([], \begin{array}{c} center & {\overset{true¯}{q}}_{x} \\ center & {\overset{true¯}{q}}_{x}^{2} true/ {\overset{true¯}{h}}_{x} + g ζ_{x} {\overset{true¯}{h}}_{x} \\ center & {\overset{true¯}{q}}_{x} {\overset{true¯}{q}}_{y} true/ {\overset{true¯}{h}}_{y} \end{array}), boldG = ([], \begin{array}{c} center & {\overset{true¯}{q}}_{y} \\ center & {\overset{true¯}{q}}_{x} {\overset{true¯}{q}}_{y} true/ {\overset{true¯}{h}}_{x} \\ center & {\overset{true¯}{q}}_{y}^{2} true/ {\overset{true¯}{h}}_{y} + g ζ_{y} {\overset{true¯}{h}}_{y} \end{array}), boldS = ([], \begin{array}{c} center & 0 \\ center & g {\overset{true¯}{h}}_{x} ((), S_{0 x} - S_{normalf x}) \\ center & g {\overset{true¯}{h}}_{y} ((), <...>) \end{array})

…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Maranzoni et al have shown that Equations to are strictly hyperbolic for h > 0 and reduce to the classic 2D SWE for free surface flows when 0 ≤ h ≤ H .…”

Section: Mathematical Modelmentioning

confidence: 99%

Section: Mathematical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Numerical treatment of a discontinuous top surface in 2D shallow water mixed flow modeling

Maranzoni

Mignosa

2017

Numerical Methods in Fluids

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show abstract

Extension of the two‐component pressure approach for modeling mixed free‐surface‐pressurized flows with the two‐dimensional shallow water equations

Cea

López-Núñez

2020

Numerical Methods in Fluids

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Numerical models based on the two‐dimensional shallow water equations (2D‐SWE) are routinely used in flood risk management and inundation studies. However, most of these models do not adequately account for vertically confined flow conditions that can appear during inundations, due to the presence of hydraulic structures such as bridges, culverts, or underground river reaches. In this article we propose a new mathematical modification of the standard 2D‐SWE, inspired by the two‐component pressure approach for 1D flows, to address the issue of transient vertically confined flows including transitions between free surface and pressurized conditions. A finite volume discretization to solve the proposed system of equations is proposed and analyzed. Various test cases are used to show the numerical stability and accuracy of the discretization, and to validate the proposed formulation. Results show that the proposed method is numerically stable, accurate, mass conservative, and preserves the C‐property. It can also handle subcritical, supercritical, and transcritical flows under free surface or vertically confined conditions.

show abstract

Modeling Transient Mixed Flows in Drainage Networks With Smoothed Particle Hydrodynamics

Song,

Yan,

Tao

et al. 2024

Water Resour Manage

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Extension and application of the Preissmann slot model to 2D transient mixed flows

Cited by 28 publications

References 36 publications

Numerical treatment of a discontinuous top surface in 2D shallow water mixed flow modeling

Numerical treatment of a discontinuous top surface in 2D shallow water mixed flow modeling

Extension of the two‐component pressure approach for modeling mixed free‐surface‐pressurized flows with the two‐dimensional shallow water equations

Modeling Transient Mixed Flows in Drainage Networks With Smoothed Particle Hydrodynamics

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