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 three settings (lid-driven cavity over a porous bed, infiltration problem and general filtration problem) with different geometrical configurations (channelised and staggered distributions of solid grains) and different sets of interface conditions. Effective parameters for the macroscale models (permeability tensor, boundary layer constants) 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.

Unsuitability of the Beavers–Joseph interface condition for filtration problems

“…In this case, the Beavers-Joseph condition (2.9) is suitable to couple the macroscale models. Rybak et al (2019) showed that this condition is also applicable when the flow is almost perpendicular to the interface. In this paper, we consider flow regimes with arbitrary flow directions (figures 1, 3 and 9) and we study different geometrical configurations for the porous-medium domain (figures 2 and 6).…”

“…To validate the applicability of the Beavers-Joseph interface condition (2.9) we evaluate cross-sections in the middle of the porous-medium domain at x 1 = 1.5 and also at x 1 = 2.2. For all simulations the fluid-porous interface Γ is located at x 2 = 0, directly on the top of the first row of solid inclusions as proposed in Lācis et al (2019) and Rybak et al (2019). The Beavers-Joseph parameter α BJ = 1 is commonly chosen in the literature.…”

“…We observe that the microscale numerical simulation results are in a good agreement with the macroscale solutions for α BJ = 1.3. We should mention that the commonly taken α BJ = 1 is not always the optimal choice (figure 5, zoom) even for the Stokes-Darcy problems where the Beavers-Joseph condition is suitable, see also Rybak et al (2019). Due to the reason that the fluid flow is almost parallel to the fluid-porous interface and the filtration into the porous medium is roughly the same along the interface Γ , velocity profiles at other cross-sections look very similar to those presented in figure 5.…”

Numerical methods for solving improper problems of filtration theory

“…is based on obtaining the decomposition of the variation dJ 2 in the independent variations dm, dλ 1 , dλ 1 [25][26][27]. We decompose the variation in independent variations.…”

A novel one-domain approach for modeling flow in a fluid-porous system including inertia and slip effects

“…Modeling one-phase flow in a coupled fluid-porous medium system has been the subject of active research since the pioneering work of Beavers and Joseph. 1,2 Applications of such a configuration are numerous, ranging from hydrology to chemical engineering. The main difficulty lies in a physically relevant way of reconciling a macroscopic description of the flow with a Darcy equation (or its variants) applicable in the bulk of the porous medium to the Navier-Stokes equation in the bulk fluid.…”