scholarly journals High Order Homogenization of the Stokes System in a Periodic Porous Medium

2021 ◽  
Vol 53 (3) ◽  
pp. 2890-2924
Author(s):  
Florian Feppon
Keyword(s):  
Porous Medium ◽  
Stokes System ◽  
High Order ◽  
Periodic Porous Medium

WEAK NONLINEAR CORRECTIONS FOR DARCY’S LAW

1996 ◽  
Vol 06 (08) ◽  
pp. 1143-1155 ◽  
Author(s):  
ALAIN BOURGEAT ◽  
EDUARD MARUŠIĆ-PALOKA ◽  
ANDRO MIKELIĆ
Keyword(s):  
Reynolds Number ◽  
Porous Medium ◽  
Asymptotic Expansion ◽  
Error Estimate ◽  
Critical Exponent ◽  
Stokes System ◽  
Navier Stokes ◽  
Order Error ◽  
Periodic Porous Medium ◽  
Local Reynolds Number

We consider the Navier-Stokes system in a periodic porous medium Ωε where ε is the characteristic pore size. The viscosity is of order εβ with 0≤β<3/2, sufficiently close to the critical exponent β=3/2. An asymptotic expansion for the velocity and the pressure, in terms of the local Reynolds number Reε=ε3−2βis set and a second-order error estimate is proved.

Application of High-Order Scheme for Flow/Acoustic Simulation at the Interface Between Air and Porous Medium

2009 ◽  
Author(s):  
Ying Xu ◽  
Z. C. Zheng
Keyword(s):  
Porous Medium ◽  
Stokes Equations ◽  
High Order ◽  
Upwind Scheme ◽  
Low Flow ◽  
High Order Scheme ◽  
High Order Schemes ◽  
Wind Turbulence ◽  
Order Scheme ◽  
Flow Resistivity

Accuracy at the interface is an important aspect in simulating air/porous medium problems for sound propagation in the atmosphere. Currently, high-order schemes have been used in simulation for viscous flow around steady and moving solid bodies, but still have not been applied to simulating flow field in different media. The study in this paper is intended to apply a high-order scheme to improve the accuracy at the interface between air and porous medium. In the vicinity of the interface, spatial derivatives of flux are discretized using different high order schemes: second-order upwind scheme, third-order upwind scheme, and 5th-order WENO scheme. The calculations are performed on a staggered Cartesian grid. The model equations for flow in the air used in this paper are the Navier-Stokes equations for incompressible flow. Flow inside the windscreen (porous medium) is modeled with a modified Zwikker-Kosten equation (Sound Absorbing Materials, 1949). An immersed-boundary method using direct forcing is utilized. The problem of flow over a solid cylinder is used as a validation case for different schemes that are implemented and compared. The application of the study is to investigate the sound pressure level reduction between unscreened microphone and screened microphone under different frequencies of incoming wind turbulence. The wind turbulence in the present work is introduced by placing different sizes of solid cylinders in the upstream of the microphone. The simulation shows that for low-frequency turbulence, the windscreens with low flow resistivity are more effective in noise reduction, while for high-frequency turbulence, the windscreens with high flow resistivity are more effective.

Self-diffusion in a periodic porous medium: A comparison of different approaches

1995 ◽  
Vol 51 (4) ◽  
pp. 3393-3400 ◽  
Author(s):  
David J. Bergman ◽  
Keh-Jim Dunn ◽  
Lawrence M. Schwartz ◽  
Partha P. Mitra
Keyword(s):  
Porous Medium ◽  
Self Diffusion ◽  
Periodic Porous Medium

Homogenisation of the Stokes problem with a pure non-homogeneous slip boundary condition by the periodic unfolding method

2011 ◽  
Vol 22 (4) ◽  
pp. 333-345 ◽  
Author(s):  
ANCA CAPATINA ◽  
HORIA ENE
Keyword(s):  
Boundary Condition ◽  
Porous Medium ◽  
Stokes System ◽  
Stokes Problem ◽  
Slip Boundary Condition ◽  
Perforated Domains ◽  
Slip Boundary ◽  
Periodic Unfolding Method ◽  
The Right ◽  
Unfolding Method

We study the homogenisation of the Stokes system with a non-homogeneous Fourier boundary condition on the boundary of the holes, depending on a parameter γ. Such systems arise in the modelling of the flow of an incompressible viscous fluid through a porous medium under the influence of body forces. At the limit, by using the periodic unfolding method in perforated domains, we obtain, following the values of γ, different Darcy's laws of typeMu= −N∇p+Fwith suitable matricesMandNwithFdepending on the right-hand side in the bulk term and in the boundary condition.

Homogenization of a non-stationary non-Newtonian flow in a porous medium containing a thin fissure

2018 ◽  
Vol 30 (2) ◽  
pp. 248-277
Author(s):  
MARÍA ANGUIANO
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Critical Case ◽  
Stokes System ◽  
Characteristic Size ◽  
Time Dependent ◽  
Darcy Law ◽  
Flow Index ◽  
Newtonian Flow ◽  
Non Linear

We consider a non-stationary incompressible non-Newtonian Stokes system in a porous medium with characteristic size of the pores ϵ and containing a thin fissure of width ηϵ. The viscosity is supposed to obey the power law with flow index$\frac{5}{3}\leq q\leq 2$. The limit when size of the pores tends to zero gives the homogenized behaviour of the flow. We obtain three different models depending on the magnitude ηϵwith respect to ϵ: if ηϵ≪$\varepsilon^{q\over 2q-1}$the homogenized fluid flow is governed by a time-dependent non-linear Darcy law, while if ηϵ≫$\varepsilon^{q\over 2q-1}$is governed by a time-dependent non-linear Reynolds problem. In the critical case, ηϵ≈$\varepsilon^{q\over 2q-1}$, the flow is described by a time-dependent non-linear Darcy law coupled with a time-dependent non-linear Reynolds problem.

Sign in / Sign up

Export Citation Format

Share Document