The solution of the dam-break problem in the Porous Shallow water Equations

Cozzolino, Luca; Pepe, Veronica; Cimorelli, Luigi; D'Aniello, Andrea; Morte, Renata Della; Pianese, Domenico

doi:10.1016/j.advwatres.2018.01.026

Cited by 27 publications

(27 citation statements)

References 35 publications

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“…This work has important analogies and differences with [22], which analyzes the behavior of the porous shallow water system, used to study the flow field when a significant part of the domain is covered by buildings, and a simplified technique avoiding a very refined grid between buildings is required. The role of the channel width is similar to the role of the porosity in the urban environment, and the configurations in the case of width changes are strictly similar.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, all the limit curves are found analytically here, and this may be an added value for classifying various cases. Finally, the numerical method presented herein is completely different from that proposed in [22]. The [23,24] general framework for nonconservative systems, within which the DOT method [25] is conceived, is considered the "natural tool" to solve the augmented shallow water system: the coupling with a proper design of a nonlinear path is the only problem-dependent (bottom elevation steps, abrupt changes in width) ingredient.…”

Section: Introductionmentioning

confidence: 99%

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Dam break in rectangular channels with different upstream-downstream widths

Valiani

Caleffi

2019

Advances in Water Resources

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The classic Stoker dam-break problem [1] is revisited in cases of different channel widths upstream and downstream of the dam. The channel is supposed to have a rectangular cross section and a horizontal and frictionless bottom. The system of the shallow water equations is enriched, using the width as a space-dependent variable, together with the depth and the unit discharge, which conversely depend on both space and time. Such a formulation allows a quasi-analytical treatment of the system, whose solution is similar to that of the classic Stoker solution when the downstream/upstream depth ratio is sufficiently large, except that a further stationary contact wave exists at the dam position. When the downstream/upstream depth ratio is small, the solution is richer than the Stoker solution because the critical state occurs at the dam position and the solution itself becomes resonant at the same position, where two eigenvalues are null and the strict hyperbolicity of the system is lost. The limits that identify the flow regime for channel contraction and channel expansion are discussed after showing that the nondimensional parameters governing the problem are the downstream/upstream width ratio and the downstream/upstream initial depth ratio.After the introduction of the previous analytical framework, a numerical analysis is also performed to evaluate a numerical method that is conceived to suitably capture rarefactions, shock waves and contact waves. A secondorder method is adopted, employing a Dumbser-Osher-Toro Riemann solver equipped with a nonlinear path. Such an original nonlinear path is shown to perform better than the classic linear path when contact waves of large amplitude must be captured, being able to obtain specific energy conservation and mass conservation at the singularity.The codes, written in MATLAB (MathWorks Inc.) language, are made available in Mendeley Data repository.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dam break in rectangular channels with different upstream-downstream widths

Valiani

Caleffi

2019

Advances in Water Resources

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“…It is possible to demonstrate [11] that the solution of the dam-break problem, i.e. the particular case of Riemann problem with initial zero velocity, depends on the definition of the geometricdiscontinuity inner-structure.…”

Section: Introductionmentioning

confidence: 99%

“…Other definitions, such as those by [12] and [13], are either internally inconsistent or imply the incompleteness of the problem solution. Interestingly, the solution of the dam-break problem always exists and it is unique if an appropriate parameterization of the stationary weak solutions of the Porous Shallow water Equations is used to supply the inner structure of the geometric discontinuity, as made in [11].…”

Section: Introductionmentioning

confidence: 99%

“…In the present paper, the exact solution of the one-dimensional Riemann problem for the Porous Shallow water Equations is presented, assuming that the right state is initially dry and that the jump definition is the same of [11]. This special Riemann problem on dry bed seems a good candidate in order to explore interesting problems encountered when the flooding of urban areas with strong porosity gradients and initial dry bed is modelled.…”

Section: Introductionmentioning

confidence: 99%

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Multiple Solutions for the Riemann Problem in the Porous Shallow Water Equations

Cozzolino¹,

Castaldo²,

Cimorelli³

et al.

EPiC Series in Engineering

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The Porous Shallow water Equations are widely used in the context of urban flooding simulation. In these equations, the solid obstacles are implicitly taken into account by averaging the classic Shallow water Equations on a control volume containing the fluid phase and the obstacles. Numerical models for the approximate solution of these equations are usually based on the approximate calculation of the Riemann fluxes at the interface between cells. In the present paper, it is presented the exact solution of the one-dimensional Riemann problem over the dry bed, and it is shown that the solution always exists, but there are initial conditions for which it is not unique. The non-uniqueness of the Riemann problem solution opens interesting questions about which is the physically congruent wave configuration in the case of solution multiplicity.Engineering

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Numerical modeling and simulation of heat transfer and fluid flow in a two-dimensional sudden expansion model using porous insert behind that

Zhao

2020

J Therm Anal Calorim

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The solution of the dam-break problem in the Porous Shallow water Equations

Cited by 27 publications

References 35 publications

Dam break in rectangular channels with different upstream-downstream widths

Dam break in rectangular channels with different upstream-downstream widths

Multiple Solutions for the Riemann Problem in the Porous Shallow Water Equations

Numerical modeling and simulation of heat transfer and fluid flow in a two-dimensional sudden expansion model using porous insert behind that

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