Two-dimensional computation of gas flow in a porous bed characterized by a porosity jump

Rochette, David; Clain, Stéphane

doi:10.1016/j.jcp.2006.03.013

Cited by 11 publications

(11 citation statements)

References 14 publications

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“…As (62) is valid for all existing cases depending on the respective values of i+1 , i , z b i and z b i+1 , it is possible to conclude that h (2) i+1/2 = 0 and (h) (2) i+1/2 = 0. Substituting (h) (1) LR , (h) (2) LR , (h)…”

Section: Estimation Of (H) (2)mentioning

confidence: 89%

“…LR and h (2) LR . A steady-state momentum balance is carried out on three cells (i −1, i and i +1) with a porosity and bottom elevation discontinuity between the cells i and i +1 (see the sketch on Figure 4).…”

Section: Estimation Of (H) (2)mentioning

confidence: 97%

“…In that sense, porosity can be used to 'represent the effect that the area subject to flooding is only a fraction of the total surface area' [1]. This approach has also been used to model gas flow across grids [2]. The first known derivation of shallow water flow [3] was very simple in that porosity was not fully taken into account in Unlike the previously quoted solvers, AS solvers do not determine the wave configuration to use the appropriate relation through each discontinuity.…”

Section: Introductionmentioning

confidence: 99%

“…In the following, the variables at the interface are so written with the superscripts (1) , (2) and (S) ; corresponding, respectively, to the variables at the interface for the first and second component of the flux vector and for the source term. The next subsection is devoted to their evaluation.…”

mentioning

confidence: 99%

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An approximate‐state Riemann solver for the two‐dimensional shallow water equations with porosity

Finaud-Guyot

Delenne

Lhomme

et al. 2009

Numerical Methods in Fluids

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SUMMARYPorAS, a new approximate-state Riemann solver, is proposed for hyperbolic systems of conservation laws with source terms and porosity. The use of porosity enables a simple representation of urban floodplains by taking into account the global reduction in the exchange sections and storage. The introduction of the porosity coefficient induces modified expressions for the fluxes and source terms in the continuity and momentum equations. The solution is considered to be made of rarefaction waves and is determined using the Riemann invariants. To allow a direct computation of the flux through the computational cells interfaces, the Riemann invariants are expressed as functions of the flux vector. The application of the PorAS solver to the shallow water equations is presented and several computational examples are given for a comparison with the HLLC solver.

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Section: Estimation Of (H) (2)mentioning

confidence: 89%

Section: Estimation Of (H) (2)mentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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An approximate‐state Riemann solver for the two‐dimensional shallow water equations with porosity

Finaud-Guyot

Delenne

Lhomme

et al. 2009

Numerical Methods in Fluids

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“…Such methods where the jacobian matrix and the nonconservative flux are combined (the Q-methods [6]) are employed in numerous applications like shallow-water [36] or porous media [28,27]. Extensions to higher-order scheme have been proposed using a ENO-WENO reconstruction or the MUSCL technique [9,12,13,37].…”

Section: Introductionmentioning

confidence: 99%

First- and second-order finite volume methods for the one-dimensional nonconservative Euler system

Clain

Rochette

2009

Journal of Computational Physics

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International audienceGas flow in porous media with a nonconstant porosity function provides a nonconservative Euler system. We propose a new class of schemes for such a system for the one-dimensional situations based on nonconservative fluxes preserving the steady-state solutions. We derive a second-order scheme using a splitting of the porosity function into a discontinuous and a regular part where the regular part is treated as a source term while the discontinuous part is treated with the nonconservative fluxes. We then present a classification of all the configurations for the Riemann problem solutions. In particularly, we carefully study the resonant situations when two eigenvalues are superposed. Based on the classification, we deal with the inverse Riemann problem and present algorithms to compute the exact solutions. We finally propose new Sod problems to test the schemes for the resonant situations where numerical simulations are performed to compare with the theoretical solutions. The schemes accuracy (first- and second-order) is evaluated comparing with a nontrivial steady-state solution with the numerical approximation and convergence curves are established

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“Smart” passive thermal insulation of confined natural convection heat transfer: An application to hollow construction blocks

Idan

Feldman

2017

Applied Thermal Engineering

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Two-dimensional computation of gas flow in a porous bed characterized by a porosity jump

Cited by 11 publications

References 14 publications

An approximate‐state Riemann solver for the two‐dimensional shallow water equations with porosity

An approximate‐state Riemann solver for the two‐dimensional shallow water equations with porosity

First- and second-order finite volume methods for the one-dimensional nonconservative Euler system

“Smart” passive thermal insulation of confined natural convection heat transfer: An application to hollow construction blocks

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