Hydrodynamical modelling and multidimensional approximation of estuarian river flows

Amara, Mohamed; Capatina-Papaghiuc, Daniela; Trujillo, David

doi:10.1007/s00791-003-0106-z

Cited by 8 publications

(16 citation statements)

References 2 publications

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“…The system dimension depends on the number of modal functions. In particular this work focuses on elliptic problems, e.g., advection-diffusion-reaction problems in pipe or channel networks (for an example of global model reduction in hydrodynamics we refer to [2]). Hierarchical local model reduction also paves the way to a model adaptation procedure which automatically detects the local level of model refinement to equilibrate, for instance, modeling and discretization errors.…”

Section: D 1dmentioning

confidence: 99%

Hierarchical Local Model Reduction for Elliptic Problems: A Domain Decomposition Approach

Perotto¹,

Ern²,

Veneziani³

2010

Multiscale Model. Simul.

119

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Some engineering applications, for instance related to fluid dynamics in pipe or channel networks, feature a dominant spatial direction along which the most relevant dynamics develop. Nevertheless, local features of the problem depending on the other directions, that we call transverse, can be locally relevant to the whole problem. We propose in the context of elliptic problems such as advection-diffusion-reaction equations, a hierarchical model reduction approach in which a coarse model featuring only the dominant direction dynamics is enriched locally by a fine model that accounts for the transverse variables via an appropriate modal expansion. We introduce a domain decomposition approach allowing us to employ a different number of modal functions in different parts of the domain according to the local complexity of the problem at hand. The methodology is investigated numerically on several test cases.

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Section: D 1dmentioning

confidence: 99%

Hierarchical Local Model Reduction for Elliptic Problems: A Domain Decomposition Approach

Perotto¹,

Ern²,

Veneziani³

2010

Multiscale Model. Simul.

119

View full text Add to dashboard Cite

show abstract

“…     h t + ∇ ∇ ∇ X X X • (hu u u) = 0, u u u t + u u u • ∇ ∇ ∇ X X X u u u + g∇ ∇ ∇ X X X h = g −∇ ∇ ∇ X X X Z − u u u u u u C(h, X X X) 2 , (1. 1) where g is the gravity constant, h the fluid height, u u u = (u 1 , u 2 ) ∈ R 2 the fluid velocity and C(h, X X X) is a 2D friction model. The unknowns h and u u u depend on the time variable t and the space variable X X X = (x 1 , x 2 ) ∈ R 2 .…”

Section: Froude Numbermentioning

confidence: 99%

“…Another problem of interest is the coupling between 1D and 2D shallow water models. Here, the goal is either to carry out a complete modeling of an estuary, see for instance [1], or to model river floods, see for instance [12]. Our model is built directly from the 2D shallow water equations, which ensures a natural coupling between the two models.…”

Section: Perspectivesmentioning

confidence: 99%

Consistent section-averaged shallow water equations with bottom friction

Michel-Dansac

Noble

Vila

2021

European Journal of Mechanics - B/Fluids

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In this paper, we present a general framework to construct section-averaged models when the flow is constrained -e.g. by topography -to be almost one-dimensional. These models are consistent with the two-dimensional shallow water equations. After rewriting the two-dimensional shallow water equations in a suitable set of coordinates allowing to take care of a meandering configuration, we consider the quasi one-dimensional regime. Then, we expand the water elevation and velocity field in the spirit of the diffusive wave equations and establish a set of one-dimensional equations made of a mass, momentum and energy equations, which are close to the ones usually used in hydraulic engineering. Our model reduces to classical shallow water models with variable sections found in the literature. Out of these configurations, there is an O(1) deviation of our model from the classical ones. Finally, we present the main mathematical properties of our model and carry out numerical simulations to validate our approach by comparing the results to the full two-dimensional shallow water equations. 1Main scaling parameter

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“…Finally, the idea of an a posteriori modeling estimator can be undoubtly made more incisive when dimensionally heterogeneous models are coupled. A first attempt in such direction has been provided in [4] and will be object of a forthcoming paper [12].…”

Section: A Look Behind and A Look Aheadmentioning

confidence: 99%

Adaptive modeling for free-surface flows

Perotto¹

2006

ESAIM: M2AN

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Abstract. This work represents a first step towards the simulation of the motion of water in a complex hydrodynamic configuration, such as a channel network or a river delta, by means of a suitable "combination" of different mathematical models. In this framework a wide spectrum of space and time scales is involved due to the presence of physical phenomena of different nature. Ideally, moving from a hierarchy of hydrodynamic models, one should solve throughout the whole domain the most complex model (with solution u fine ) to accurately describe all the physical features of the problem at hand. In our approach instead, for a user-defined output functional F, we aim to approximate, within a prescribed tolerance τ , the value F(u fine ) by means of the quantity F(u adapted ), u adapted being the so-called adapted solution solving the simpler models on most of the computational domain while confining the complex ones only on a restricted region. Moving from the simplified setting where only two hydrodynamic models, fine and coarse, are considered, we provide an efficient tool able to automatically select the regions of the domain where the coarse model rather than the fine one are to be solved, while guaranteeing |F(u fine ) − F(u adapted )| below the tolerance τ . This goal is achieved via a suitable a posteriori modeling error analysis developed in the framework of a goal-oriented theory. We extend the dual-based approach provided in [Braack and Ern, Multiscale Model Sim. 1 (2003) 221-238], for steady equations to the case of a generic time-dependent problem. Then this analysis is specialized to the case we are interested in, i.e. the free-surface flows simulation, by emphasizing the crucial issue of the time discretization for both the primal and the dual problems. Finally, in the last part of the paper a widespread numerical validation is carried out.Mathematics Subject Classification. 65J15, 65M15, 65M60.

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Hydrodynamical modelling and multidimensional approximation of estuarian river flows

Cited by 8 publications

References 2 publications

Hierarchical Local Model Reduction for Elliptic Problems: A Domain Decomposition Approach

Hierarchical Local Model Reduction for Elliptic Problems: A Domain Decomposition Approach

Consistent section-averaged shallow water equations with bottom friction

Adaptive modeling for free-surface flows

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