Asymptotic study for Stokes–Brinkman model with jump embedded transmission conditions

Angot, Philippe; Péron, Victor

doi:10.3233/asy-151336

Cited by 8 publications

(14 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the context of pore-scale modeling, this formulation take into account both the fluid region inside the pores and the (small) porosity of the surrounding matrix: it is a two-scale model. Furthermore, such a term can be used as a penalization technique in order to satisfy a no-slip condition at the fluid/solid interface [48,3], by choosing a value of ε that is as small as possible (given the robustness of the numerical method used, since the problem becomes stiffer as ε decreases).…”

Section: Superficial Velocitymentioning

confidence: 99%

“…), while volume reactions allow most of the usual numerical methods (including LBM [58,27], FV [51] and SPH [7]) but require clever modeling of surfacelocalized phenomena. Volume based modeling using structured meshes can involve crude no-slip conditions fusing penalization techniques [3,16], but nowadays two-scale models are suitably formalized [42,38,51], allowing greater physical involvement of the rock matrix in the samples.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Improvement of remeshed Lagrangian methods for the simulation of dissolution processes at pore-scale

Etancelin

Moonen

Poncet

2020

Advances in Water Resources

View full text Add to dashboard Cite

This article shows how to consistently and accurately manage the Lagrangian formulation of chemical reaction equations coupled with the superficial velocity formalism introduced in the late 80s by Quintard and Whitaker. Lagrangian methods prove very helpful in problems in which transport effects are strong or dominant, but they need to be periodically put back in a regular lattice, a process called remeshing. In the context of digital rock physics, we need to ensure positive concentrations and regularity to accurately handle stagnation point neighborhoods. These two conditions lead to the use of kernels resulting in extra-diffusion, which can be prohibitively high when the diffusion coefficient is small. This is the case especially for reactive porous media, and the phenomenon is reinforced in porous rock matrices due to Archie's law. This article shows how to overcome this difficulty in the context of a two-scale porosity model applied in the Darcy-Brinkman-Stokes equations, and how to obtain simultaneous sign preservation, regularity and accurate diffusion, and apply it to dissolution processes at the pore scale of actual rocks.

show abstract

Section: Superficial Velocitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Improvement of remeshed Lagrangian methods for the simulation of dissolution processes at pore-scale

Etancelin

Moonen

Poncet

2020

Advances in Water Resources

View full text Add to dashboard Cite

show abstract

“…[17]) the solution to the limit problem (3.11) can be view as the zeroth order exterior expansion and is used to approximate the solution outside the boundary layer. Similar singular perturbation problem involving Stokes-Brinkman interface model has been studied in [5] where the author compute boundary layer corrector as well as the complete asymptotic expansion. Nevertheless, this paper aims at using the model (2.3) for topology optimization to be able to look for optimal design that are porous medium.…”

Section: )mentioning

confidence: 99%

“…[20]). For instance the Brinkman model [5] involves a second order term, with an effective viscosity, in the porous medium and can be used to account high porosity of the porous media. Another example is the Forchheimer model [14] whose model involves an additional non-linear term inside the porous media to deal with microscopic inertial effects.…”

Section: )mentioning

confidence: 99%

Penalization model for Navier–Stokes–Darcy equations with application to porosity-oriented topology optimization

Bastide

Cocquet

Ramalingom

2018

Math. Models Methods Appl. Sci.

View full text Add to dashboard Cite

Topology optimization for fluid flow aims at finding the location of a porous medium minimizing a cost functional under constraints given by the Navier–Stokes equations. The location of the porous media is usually taken into account by adding a penalization term [Formula: see text], where [Formula: see text] is a kinematic viscosity divided by a permeability and [Formula: see text] is the velocity of the fluid. The fluid part is obtained when [Formula: see text] while the porous (solid) part is defined for large enough [Formula: see text] since this formally yields [Formula: see text]. The main drawback of this method is that only solid that does not let the fluid to enter, that is perfect solid, can be considered. In this paper, we propose to use the porosity of the media as optimization parameter hence to minimize some cost function by finding the location of a porous media. The latter is taken into account through a singular perturbation of the Navier–Stokes equations for which we prove that its weak-limit corresponds to an interface fluid-porous medium problem modeled by the Navier–Stokes–Darcy equations. This model is then used as constraint for a topology optimization problem. We give necessary condition for such problem to have at least an optimal solution and derive first order necessary optimality condition. This paper ends with some numerical simulations, for Stokes flow, to show the interest of this approach.

show abstract

“…Using the ratio of pore size to the macroscopic length scale as a small parameter, the dominant jump conditions are found at the first order, and the generality of such asymptotic analysis allows them to make direct comparison with several pre-existing models such as the pioneering slip model by Beavers and Joseph 21 . It is worth mentioning that the approach adopted by Angot et al [22][23][24] was suggested by Worster et al 25,26 , where the empirical formula for the jump boundary conditions is similar to those used and/or derived in many other works [27][28][29][30][31][32][33][34][35][36][37] .…”

Section: Introductionmentioning

confidence: 99%

Slightly deformable Darcy drop in linear flows

2019

View full text Add to dashboard Cite

The small-deformation of a poroelastic drop due to an external linear flow field in the suspending medium is investigated. A two-phase flow model is developed to study the small-deformation of such a poroelastic drop under linear flows. Inside the drop a deformable porous network with a bending rigidity and a viscosity is fully immersed in a viscous fluid. When the viscous dissipation of the interior fluid phase is negligible (compared to the friction between the fluid and the skeleton), the two-phase flow is reduced to a poroelastic Darcy fluid with a deformable porous network. At the interface between the poroelastic drop and the exterior Stokesian fluid, a novel set of boundary conditions are derived by the free energy dissipation principle. Both slip and permeability are taken into account and the permeating flow induces dissipation that depends on the elastic stress of the interior solid. Assuming that the porous network is slightly deformed from its original spherical shape due to its large bending rigidity, a small-deformation analysis is conducted. A steady equilibrium is computed for two different linear flows: a uniaxial extensional flow and a planar shear flow. By exploring the interfacial slip, permeability and network elasticity various flow patterns are found at equilibrium of these slightly deformed poroelastic drops. Linear dynamics of the small-amplitude deviation of the poroelastic drop from the spherical shape is governed by a nonlinear eigenvalue problem, and the eigenvalues are determined numerically, and asymptotically in certain limits. These results lay the foundation for studying the rheology of a suspension of poroelastic spherical particles, and give insight to possible flow patterns of a system of selfpropelling swimmers with porous flow (such as intracellular cytosol) inside.

show abstract

Asymptotic study for Stokes–Brinkman model with jump embedded transmission conditions

Cited by 8 publications

References 8 publications

Improvement of remeshed Lagrangian methods for the simulation of dissolution processes at pore-scale

Improvement of remeshed Lagrangian methods for the simulation of dissolution processes at pore-scale

Penalization model for Navier–Stokes–Darcy equations with application to porosity-oriented topology optimization

Slightly deformable Darcy drop in linear flows

Contact Info

Product

Resources

About