Stability of natural convection in superposed fluid and porous layers: Equivalence of the one- and two-domain approaches

Hirata, Sílvia C.; Goyeau, Benoı̂t; Gobin, D.; Chandesris, Marion; Jamet, Dominique

doi:10.1016/j.ijheatmasstransfer.2008.07.045

Cited by 39 publications

(40 citation statements)

References 17 publications

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“…Hirata et al 2007bHirata et al , 2009bHill & Straughan 2009), is captured in figure 3. In this bimodal behaviour, the fluid mode (corresponding to perturbations of large wavenumbers) relates to the case where the convective flow is mainly confined in the fluid layer, with the porous mode (corresponding to perturbations of small wavenumbers) relating to the case where the convective flow occurs in the entire porous region.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…System (2.1) is equivalent to adopting the Navier-Stokes and the Darcy-Brinkman equations to govern the flow in the fluid domain and the porous region, respectively, cf. Hirata et al (2007bHirata et al ( , 2009b.…”

Section: Formation Of the Problemmentioning

confidence: 99%

“…Goyeau et al (2003) and Hirata et al (2007bHirata et al ( , 2009b. However, this approach precludes the direct construction of a nonlinear stability threshold, as it prevents the use of the divergence theorem (which will be discussed in §3b).…”

Section: Formation Of the Problemmentioning

confidence: 99%

“…Comparisons between the one-and twodomain approaches and the subsequent treatment of the interfacial region are discussed in Goyeau et al (2003) and Hirata et al (2007b). The equivalence of the one-and two-domain approaches for the Darcy-Brinkman/Navier-Stokes model is shown in Hirata et al (2009b).…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear stability of the one-domain approach to modelling convection in superposed fluid and porous layers

Hill

Carr

2010

Proc. R. Soc. A.

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Studies of the nonlinear stability of fluid/porous systems have been developed very recently. A two-domain modelling approach has been adopted in previous works, but was restricted to specific configurations. The extension to the more general case of a Navier-Stokes modelled fluid over a porous material was not achieved for the twodomain approach owing to the difficulties associated with handling the interfacial boundary conditions. This paper addresses this issue by adopting a one-domain approach, where the governing equations for both regions are combined into a unique set of equations that are valid for the entire domain. It is shown that the nonlinear stability bound, in the one-domain approach, is very sharp and hence excludes the possibility of subcritical instabilities. Moreover, the one-domain approach is compared with an equivalent two-domain approach, and excellent agreement is found between the two.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Formation Of the Problemmentioning

confidence: 99%

Section: Formation Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear stability of the one-domain approach to modelling convection in superposed fluid and porous layers

Hill

Carr

2010

Proc. R. Soc. A.

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“…The eigenvalue problem has been solved using the generalized integral transform technique, GITT (Cotta 1993). For conciseness, the stability analysis and the GITT are not described in this article and details can be found in Hirata et al (2009).…”

Section: Thermal Natural Convectionmentioning

confidence: 99%

On the Equivalence of the Discontinuous One- and Two-Domain Approaches for the Modeling of Transport Phenomena at a Fluid/Porous Interface

2008

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In the quest (i) to determine the form of the boundary conditions that must be applied at a fluid/porous interface and (ii) to determine the value of the jump parameters that appear in the expression for these boundary conditions, two different approaches are commonly considered: the so-called one-domain and two-domain approaches. These approaches are commonly thought to be different, and they are thus sometimes compared to each other to determine the value of jump parameters. In this article, we show that the two-domain and discontinuous one-domain approaches are actually strictly equivalent, provided that the latter is mathematically interpreted in the sense of distributions. This equivalence is shown in details for a heat conduction problem and for the more classical Darcy-Brinkman problem. We show in particular that interfacial jumps are introduced in the discontinuous one-domain approach through Dirac delta functions. Numerical issues are then discussed that show that subtle discretization truncation errors give rise to large variations that can be mis-interpreted as the sign of the existence of jump parameters.

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Vertical dispersion in vegetated shear flows

Rubol

Battiato²,

Barros

2016

Water Resour. Res.

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Canopy layers control momentum and solute transport to and from the overlying water surface layer. These transfer mechanisms strongly dependent on canopy geometry, affect the amount of solute in the river, the hydrological retention and availability of dissolved solutes to organisms located in the vegetated layers, and are critical to improve water quality. In this work, we consider steady state transport in a vegetated channel under fully developed flow conditions. Under the hypothesis that the canopy layer can be described as an effective porous medium with prescribed properties, i.e., porosity and permeability, we model solute transport above and within the vegetated layer with an advection‐dispersion equation with a spatially variable dispersion coefficient (diffusivity). By means of the Generalized Integral Transform Technique, we derive a semianalytical solution for the concentration field in submerged vegetated aquatic systems. We show that canopy layer's permeability affects the asymmetry of the concentration profile, the effective vertical spreading behavior, and the magnitude of the peak concentration. Due to its analytical features, the model has a low computational cost. The proposed solution successfully reproduces previously published experimental data.

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Stability of natural convection in superposed fluid and porous layers: Equivalence of the one- and two-domain approaches

Cited by 39 publications

References 17 publications

Nonlinear stability of the one-domain approach to modelling convection in superposed fluid and porous layers

Nonlinear stability of the one-domain approach to modelling convection in superposed fluid and porous layers

On the Equivalence of the Discontinuous One- and Two-Domain Approaches for the Modeling of Transport Phenomena at a Fluid/Porous Interface

Vertical dispersion in vegetated shear flows

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