A Darcy-Brinkman model of flow in double porous media – Two-level homogenization and computational modelling

Rohan, Eduard; Turjanicová, Jana; Lukeš, Vladimír

doi:10.1016/j.compstruc.2017.08.006

Cited by 12 publications

(13 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The effective coefficients of the mesoscopic model are computed according to (22)- (23), so that the characteristic responses (31) and (32) of the periodic mesoscopic structure can be resolved. Consequently, the effective coefficients of the macroscopic model are evaluated using (33)- (35).…”

Section: Results Of the Simulationmentioning

confidence: 99%

See 1 more Smart Citation

The Biot–Darcy–Brinkman model of flow in deformable double porous media; homogenization and numerical modelling

Rohan

Turjanicová

Lukeš

2019

Computers & Mathematics with Applications

Self Cite

View full text Add to dashboard Cite

In this paper we present the two-level homogenization of the flow in a deformable doubleporous structure described at two characteristic scales. The higher level porosity associated with the mesoscopic structure is constituted by channels in a matrix made of a microporous material consisting of elastic skeleton and pores saturated by a viscous fluid. The macroscopic model is derived by the homogenization of the flow in the heterogeneous structure characterized by two small parameters involved in the two-level asymptotic analysis, whereby a scaling ansatz is adopted to respect the pore size differences. The first level upscaling of the fluid-structure interaction problem yields a Biot continuum describing the mesoscopic matrix coupled with the Stokes flow in the channels. The second step of the homogenization leads to a macroscopic model involving three equations for displacements, the mesoscopic flow velocity and the micropore pressure. Due to interactions between the two porosities, the macroscopic flow is governed by a Darcy-Brinkman model comprising two equations which are coupled with the overall equilibrium equation respecting the hierarchical structure of the two-phase medium. Expressions of the effective macroscopic parameters of the homogenized double-porosity continuum are derived, depending on the characteristic responses of the mesoscopic structure. Some symmetry and reciprocity relationships are shown and issues of boundary conditions are discussed. The model has been implemented in the finite element code SfePy which is well-suited for computational homogenization. A numerical example of solving a nonstationary problem using mixed finite element method is included.

show abstract

Section: Results Of the Simulationmentioning

confidence: 99%

“…Further note thatψ ij ∈ H 1 # (Z c ). Then (ii) follows upon introducingψ ij andφ ij in (59) which, thus, become identical with (32).…”

Section: Local Characteristic Responsesmentioning

confidence: 99%

The Biot–Darcy–Brinkman model of flow in deformable double porous media; homogenization and numerical modelling

Rohan

Turjanicová

Lukeš

2019

Computers & Mathematics with Applications

Self Cite

View full text Add to dashboard Cite

show abstract

“…It is worth to note that, due to the linearization and decoupling in three subproblems, (44)-(45), (47) and (49) present stanard boundary conditions on interface Γ ε , rather than transmission conditions, as in problem (20)- (28).…”

Section: Perturbed State Quantitiesmentioning

confidence: 99%

“…This enables us to apply the decomposed forms of the fluctuating two-scale functions in (58)-(59) u 0 , P 0 , Φ 0 α , α = 1, 2 defined in domain Ω with the local characteristic responses (corrector basis functions) defined in Y . The local microscopic fields are given by the so-called folding mapping ( [28]), such that…”

Section: Reconstruction Of Macroscopic Solution On Microstructure Levelmentioning

confidence: 99%

Homogenization based two-scale modelling of ionic transport in fluid saturated deformable porous media

Turjanicová

Rohan

Lukeš

2019

Computers & Mathematics with Applications

Self Cite

View full text Add to dashboard Cite

The paper deals with the homogenization of deformable porous media saturated by twocomponent electrolytes. The model relevant to the microscopic scale describes steady states of the medium while reflecting essential physical phenomena, namely electrochemical interactions in a dilute Newtonian solvent under assumptions of a small external electrostatic field and slow flow. The homogenization is applied to a linearized micromodel, whereby the thermodynamic equilibrium represents the reference state. Due to the dimensional analysis, scaling of the viscosity and electric permitivity is introduced, so that the limit model retains the characteristic length associated with the pore size and the electric double layer thickness. The homogenized model consists of two weakly coupled parts: the flow of the electrolyte can be solved in terms of a global pressure and streaming potentials of the two ions, independently of then the solid phase deformations which is computed afterwards for the fluid stress acting on pore walls. The two-scale model has been implemented in the Sfepy finite element software. The numerical results show dependence of the homogenized coefficients on the microstructure porosity. By virtue of the corrector result of the homogenization, microscopic responses in a local representative cell can be reconstructed from the macroscopic solutions.

show abstract

“…In the published literature, most of the research has been conducted on dual‐scale models where a simple naming scheme is utilized to denote the different length scales: fine and coarse. These will also be used in context throughout this work as modeling across 3 scales is quite rare in the literature (Fish & Yu, ; Rohan, Turjanicová, & Lukeš, ).…”

Section: Food Structurementioning

confidence: 99%

Multiscale Modeling for Food Drying: State of the Art

Welsh

Simpson

Khan

et al. 2018

Comp Rev Food Sci Food Safe

View full text Add to dashboard Cite

Plant-based food materials are mostly porous in nature and heterogeneous in structure with huge diversity in cellular orientation. Different cellular environments of plant-based food materials, such as intercellular, intracellular, and cell wall environments, hold different proportions of water with different characteristics. Due to this structural heterogeneity, it is very difficult to understand the drying process and associated morphological changes during drying. Transport processes and morphological changes that take place during drying are mainly governed by the characteristics of and the changes in the cells. Therefore, to predict the actual heat and mass transfer process that occurs in the drying process and associated morphological changes, development of multiscale modeling is crucial. Multiscale modeling is a powerful approach with the ability to incorporate this cellular structural heterogeneity with microscale heat and mass transfer during drying. However, due to the huge complexity involved in developing such a model for plant-based food materials, the studies regarding this issue are very limited. Therefore, we aim in this article to develop a critical conceptual understanding of multiscale modeling frameworks for heterogeneous food materials through an extensive literature review. We present a critical review on the multiscale model formulation and solution techniques with their spatial and temporal coupling options. Food structure, scale definition, and the current status of multiscale modeling are also presented, along with other key factors that are critical to understanding and developing an accurate multiscale framework. We conclude by presenting the main challenges for developing an accurate multiscale modeling framework for food drying.

show abstract

A Darcy-Brinkman model of flow in double porous media – Two-level homogenization and computational modelling

Cited by 12 publications

References 33 publications

The Biot–Darcy–Brinkman model of flow in deformable double porous media; homogenization and numerical modelling

The Biot–Darcy–Brinkman model of flow in deformable double porous media; homogenization and numerical modelling

Homogenization based two-scale modelling of ionic transport in fluid saturated deformable porous media

Multiscale Modeling for Food Drying: State of the Art

Contact Info

Product

Resources

About