Simulation of Coupled Viscous and Porous Flow Problems

Gartling, D. K.; Hickox, C. E.; Givler, Richard C.

doi:10.1080/10618569608940751

Cited by 103 publications

(81 citation statements)

References 15 publications

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“…Examples of direct numerical simulation of these equations in a non-vuggy context (i.e., in a medium with at most a few very large vugs) can be found in, e.g., [25,13,19]. In a vuggy context, see, e.g., [3].…”

Section: Introductionmentioning

confidence: 99%

Homogenization of a Darcy–Stokes system modeling vuggy porous media

2006

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Abstract. We derive a macroscopic model for single phase, incompressible, viscous fluid flow in a porous medium with small cavities called vugs. We model the vuggy medium on the microscopic scale using Stokes equations within the vugular inclusions, Darcy's law within the porous rock, and a Beavers-Joseph-Saffman boundary condition on the interface between the two regions. We assume periodicity of the medium, and obtain uniform energy estimates independent of the period. Through a two-scale homogenization limit as the period tends to zero, we obtain a macroscopic Darcy's law governing the medium on larger scales. We also develop some needed generalizations of the two-scale convergence theory needed for our bi-modal medium, including a two-scale convergence result on the Darcy-Stokes interface. The macroscopic Darcy permeability is computable from the solution of a cell problem. An analytic solution to this problem in a simple geometry suggests that: (1) flow along vug channels is primarily Poiseuille with a small perturbation related to the Beavers-Joseph slip, and (2) flow that alternates from vug to matrix behaves as if the vugs have infinite permeability.

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Section: Introductionmentioning

confidence: 99%

Homogenization of a Darcy–Stokes system modeling vuggy porous media

2006

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“…Numerical solutions for the coupled viscous and porous flows have been attempted by many researchers [2,3,4,12]. Different numerical methods such as finite volume method and finite element method have been used.…”

Section: Introductionmentioning

confidence: 99%

A numerical method for flows in porous and homogenous fluid domains coupled at the interface by stress jump

Lee

Zeng

et al. 2006

Numerical Methods in Fluids

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Abstract:A numerical model was developed for flows involving an interface between a homogenous fluid and a porous medium. The numerical model is based on the finite volume method with body-fitted and multi-block grids. The Darcy-Forchheimer extended model is used to govern the flow in the porous medium region. At its interface, a shear stress jump was imposed, together with a continuity of normal stress. Furthermore, the effect of the jump condition on the diffusive flux is considered, additional to that on the convective part which has been usually considered. Numerical results of three flow configurations are presented. The modeling is suitable for problems which have complex interface boundary conditions coupling between two flow domains.

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“…For modeling flow in non-deformable porous media, the Brinkman terms in the fluid momentum equations (cf. Gartling et al 1995) may be activated. Alternatively, the generalized convection diffusion equations may be transformed into Darcy transport equations, which can be used for simulations of deformable porous media.…”

Section: Jacobian Matrix Couplingmentioning

confidence: 99%

GOMA - A full-Newton finite element program for free and moving boundary problems with coupled fluid/solid momentum, energy, mass, and chemical species transport: User`s guide

Schunk¹,

Sackinger²,

Rao³

1996

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GOMA is a two-and three-dimensional finite element program which excels in analyses of manufacturing processes, particularly those involving free or moving interfaces. Specifically, the fullNewton-coupled heat, mass, momentum, and pseudo-solid mesh motion algorithm makes GOMA ideally suited for simulating processes in which the bulk fluid transport is closely coupled to the interfacial physics. Examples include, but are not limited to, coating and polymer processing flows, soldering, crystal growth, and solid-network or solution f i l m drying. The code is based on the premise that any boundary can be (1) moving or free, with an apriori unknown position dictated by the distinguishing physics, (2) fixed, according to a global analytical representation, or (3) moving in time and space under user-prescribed kinematics. The goal is to enable the user to predict boundary position or motion simultaneously with the physics of the problem being analyzed and to pursue geometrical design studies and fluid-structure interaction problems.The moving mesh algorithm treats the entire domain as a computational Lagrangian solid that deforms subject to the physical principles which dictate boundary position. As an added benefit, the same Lagrangian solid mechanics can be exploited to solve multi-field problems for which the solid motion and stresses interact with other transport phenomena, either within the same material phase (e.g. shrinking coating) or in neighboring material phases (e.g. flexible blade coating). Thus, analyses of many fluid-structure interaction problems and deformable porous media problems are accessible.This document serves as a user's guide and reference for GOMA and provides a brief overview of GOMA's capabilities, theoretical background, and classes of problems for which it is targeted. Melting conjugate problem geometry and boundary conditions. 88

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Simulation of Coupled Viscous and Porous Flow Problems

Cited by 103 publications

References 15 publications

Homogenization of a Darcy–Stokes system modeling vuggy porous media

Homogenization of a Darcy–Stokes system modeling vuggy porous media

A numerical method for flows in porous and homogenous fluid domains coupled at the interface by stress jump

GOMA - A full-Newton finite element program for free and moving boundary problems with coupled fluid/solid momentum, energy, mass, and chemical species transport: User`s guide

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