Analytical and numerical solutions of the Local Inertial Equations

Martins, Ricardo; Leandro, Jorge; Djordjević, Slobodan

doi:10.1016/j.ijnonlinmec.2016.01.015

Cited by 10 publications

(7 citation statements)

References 18 publications

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“…In the same paper, it was given a novel stability condition where both flow depth and velocity were taken into account, but again no theoretical justification was given. In Martins et al (2016a), a Finite Volume scheme based on the Roe Riemann solver and a MacCormack finite difference scheme were tested using the dambreak exact solution. The results showed that numerical algorithms written in conservative form are able to reproduce moving discontinuities arising in LInA, but the treatment of the wetting-drying fronts was not clearly specified.…”

Section: Introductionmentioning

confidence: 99%

Flood propagation modeling with the Local Inertia Approximation: Theoretical and numerical analysis of its physical limitations

Cozzolino

Cimorelli

Morte

et al. 2019

Advances in Water Resources

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Attention of the researchers has increased towards a simplification of the complete Shallow waterEquations called the Local Inertia Approximation (LInA), which is obtained by neglecting the advection term in the momentum conservation equation. This model, whose physical basis is discussed here, is commonly used for the simulation of slow flooding phenomena characterized by small velocities and absence of flow discontinuities. In the present paper it is demonstrated that a shock is always developed at moving wetting-drying frontiers, and this justifies the study of the

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Section: Introductionmentioning

confidence: 99%

Flood propagation modeling with the Local Inertia Approximation: Theoretical and numerical analysis of its physical limitations

Cozzolino

Cimorelli

Morte

et al. 2019

Advances in Water Resources

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“…In the sequence, they use an operator splitting technique to extend to a two-dimensional case. Martins et al [16] solved the Local Inertial Equations in flood hydrodynamic modeling obtained by neglecting the convective terms in the Saint-Venant equations. According to the authors neglecting these terms do not impair the problem accuracy.…”

Section: Introductionmentioning

confidence: 99%

A New Constitutive Relation for Describing the Flow through Porous Media with Unsaturated–Saturated Transition

Martins‐Costa

Silva

et al. 2019

Mathematical Problems in Engineering

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The present work proposes an adequate constitutive relation to treat the process of filling with a fluid porous medium. This relation assures the problem to remain hyperbolic when the porous medium is saturated by the fluid. When the fluid fraction reaches porosity, the proposed constitutive relation increases the porous matrix resistance to more fluid inlet due to an important feature: it is a continuous and differentiable function with first derivative being also an increasing function. This allows assuring that the fluid fraction may exceed the porosity only by a very small value, making the constitutive relation realistic. Some examples compare this new constitutive relation with previous ones, highlighting its advantages.

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“…Some authors showed that models based on the Locally Inertial Formulation are more robust than the ones based on the full SWE. Locally Inertial Formulation show a similar overall accuracy to SWE, with a significant decrease in computational time (Aronica et al ., ; Bates et al ., ; Neal et al ., ), which is in accordance with recent studies on the analytical solutions for subcritical flows (Martins et al ., , ).…”

Section: Introductionmentioning

confidence: 99%

Influence of sewer network models on urban flood damage assessment based on coupled 1D/2D models

Martins

Leandro

Djordjević

2016

J Flood Risk Management

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One of the main steps in assessing flood risk in urbanised areas is the quantification of damage costs. Damage is often estimated based on depth-damage curves for which depth maps are obtained (ideally) from coupled flood models. While the comparative analysis of flood damage models has been extensively researched in the literature, the influence of the underlying sewer network model has not been investigated. In this study, a 2D locally inertial equations flood risk analysis model (GWM) is coupled with two stormwater models (SWMM, tested with three different configurations, and SIPSON). The assessment of the network performance is made through the total exchanged volume between the surface and stormwater system, the surcharged conduits and manholes, maximum overland inundation and costs using a stepped version of the multi-coloured manual depth-damage curves for continuous urban fabric. The models behave similarly; however, they do show differences in the head pressures, number of surcharged manholes and maximum depth in some locations. The case study results show that despite the good agreement in damage between the four configurations (≈6% maximum disagreement), some localised high differences in maximum depth observed [0.25 (m)] exist. It was also shown that SWMM needs to be calibrated in order to perform similarly to Preissmann slot models.

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Analytical and numerical solutions of the Local Inertial Equations

Cited by 10 publications

References 18 publications

Flood propagation modeling with the Local Inertia Approximation: Theoretical and numerical analysis of its physical limitations

Flood propagation modeling with the Local Inertia Approximation: Theoretical and numerical analysis of its physical limitations

A New Constitutive Relation for Describing the Flow through Porous Media with Unsaturated–Saturated Transition

Influence of sewer network models on urban flood damage assessment based on coupled 1D/2D models

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