Validation and calibration of coupled porous-medium and free-flow problems using pore-scale resolved models

Abstract

The correct choice of interface conditions and effective parameters for coupled macroscale free-flow and porous-medium models is crucial for a complete mathematical description of the problem under consideration and for accurate numerical simulation of applications. We consider single-fluid-phase systems described by the Stokes-Darcy model. Different sets of coupling conditions for this model are available. However, the choice of these conditions and effective model parameters is often arbitrary. We use large scale lattice Boltzmann simulations to validate coupling conditions by comparison of the macroscale simulations against pore-scale resolved models. We analyse two settings (lid driven cavity over a porous bed and infiltration problem) with different geometrical configurations (channelised and staggered distributions of solid grains) and different sets of interface conditions. Effective parameters for the macroscale models are computed numerically for each geometrical configuration. Numerical simulation results demonstrate the sensitivity of the coupled Stokes-Darcy problem to the location of the sharp fluid-porous interface, the effective model parameters and the interface conditions.

Effective coupling conditions for arbitrary flows in Stokes-Darcy systems

“…Within this paper, two interface locations (fig. 1b) are investigated: i) the interface Σ d is located directly on top of the first row of solid obstacles as proposed in the literature for circular solid inclusions [24,36] and ii) the interface Σ 0 is located on top of the periodicity cells (x 2 = 0) which is the same position as for the new coupling conditions. Numerical simulation results for the Stokes-Darcy problem with the classical interface conditions are labeled according to the interface location (profiles: macroscale, Σ d or macroscale, Σ 0 ).…”

“…The Stokes-Darcy problem is well studied for isotropic porous media (interface location, fitting of parameter α, see e.g. [25,29,36]). However, this is not the case for anisotropic media.…”

“…The exact location of the sharp fluid-porous interface is uncertain as well. There exist several recommendations for the interface location in the literature [24,36], however, only for circular solid grains leading to isotropic porous media.…”