Influence of wall roughness on the slip behaviour of viscous fluids

2008 ◽  
Vol 138 (5) ◽  
pp. 957-973 ◽  
Author(s):  
Dorin Bucur ◽  
Eduard Feireisl ◽  
Šárka Nečasová
Keyword(s):  
Boundary Condition ◽  
Viscous Fluid ◽  
Boundary Conditions ◽  
Limit Problem ◽  
Viscous Fluids ◽  
Wall Roughness ◽  
Effective Boundary ◽  
Specific Direction ◽  
Friction Term ◽  
Effective Boundary Conditions

We consider the stationary equations of a general viscous fluid in an infinite (periodic) slab supplemented with Navier's boundary condition with a friction term on the upper part of the boundary. In addition, we assume that the upper part of the boundary is described by a graph of a function φε, where φε oscillates in a specific direction with amplitude proportional to ε. We identify the limit problem when ε → 0, in particular, the effective boundary conditions.

scholarly journals A framework for computing effective boundary conditions at the interface between free fluid and a porous medium

2017 ◽  
Vol 812 ◽  
pp. 866-889 ◽  
Author(s):  
Uǧis Lācis ◽  
Shervin Bagheri
Keyword(s):  
Boundary Condition ◽  
Porous Medium ◽  
Boundary Conditions ◽  
Stokes Equations ◽  
Accurate Method ◽  
Free Fluid ◽  
Computational Domain ◽  
Porous Bed ◽  
Effective Boundary ◽  
Effective Boundary Conditions

Interfacial boundary conditions determined from empirical or ad hoc models remain the standard approach to model fluid flows over porous media, even in situations where the topology of the porous medium is known. We propose a non-empirical and accurate method to compute the effective boundary conditions at the interface between a porous surface and an overlying flow. Using a multiscale expansion (homogenization) approach, we derive a tensorial generalized version of the empirical condition suggested by Beavers & Joseph (J. Fluid Mech., vol. 30 (01), 1967, pp. 197–207). The components of the tensors determining the effective slip velocity at the interface are obtained by solving a set of Stokes equations in a small computational domain near the interface containing both free flow and porous medium. Using the lid-driven cavity flow with a porous bed, we demonstrate that the derived boundary condition is accurate and robust by comparing an effective model to direct numerical simulations. Finally, we provide an open source code that solves the microscale problems and computes the velocity boundary condition without free parameters over any porous bed.

Effective boundary conditions for compressible flows over rough boundaries

2015 ◽  
Vol 25 (07) ◽  
pp. 1257-1297 ◽  
Author(s):  
Giulia Deolmi ◽  
Wolfgang Dahmen ◽  
Siegfried Müller
Keyword(s):  
Boundary Conditions ◽  
Compressible Flows ◽  
Incompressible Flows ◽  
Laminar Flows ◽  
Small Scale ◽  
Reynolds Number Flow ◽  
Effective Boundary ◽  
Effective Boundary Conditions ◽  
High Reynolds ◽  
Rough Boundaries

Simulations of a flow over a roughness are prohibitively expensive for small-scale structures. If the interest is only on some macroscale quantity it will be sufficient to model the influence of the unresolved microscale effects. Such multiscale models rely on an appropriate upscaling strategy. Here the strategy originally developed by Achdou et al. [Effective boundary conditions for laminar flows over periodic rough boundaries, J. Comput. Phys. 147 (1998) 187–218] for incompressible flows is extended to compressible high Reynolds number flow. For proof of concept a laminar flow over a flat plate with partially embedded roughness is simulated. The results are compared with computations on a rough domain.

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