Validation and calibration of coupled porous-medium and free-flow problems using pore-scale resolved models
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Validation and calibration of coupled porous-medium and free-flow problems using pore-scale resolved models Iryna Rybak1
¨ 2,3 · Christoph Schwarzmeier2 · Elissa Eggenweiler1 · Ulrich Rude
Received: 14 June 2019 / Accepted: 6 August 2020 © The Author(s) 2020
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. Keywords Stokes equations · Darcy’s law · Interface conditions · Lattice Boltzmann method Mathematics Subject Classification (2010) 68N99 · 76D07 · 76M50 · 76S05
1 Introduction Coupled flow systems containing a porous-medium domain and a free-flow region appear in various environmental and technical applications, such as surface-water/groundwater flow, industrial filtration and water management in fuel cells. The interaction between the flow regions is dominated by the interface driven processes and, due to their complexity, modelling such coupled flow systems is a challenging task. Different spatial scales can be employed to investigate coupled free-flow and porous-medium systems. At the microscale (pore scale) the pore structure is fully resolved (Fig. 1, left) and the flow in the entire fluid domain (free-flow region and pore space in the porous medium) is described by the Navier–Stokes equations with the no-
Iryna Rybak
[email protected]
Extended author information available on the last page of the article.
slip condition at the boundary of the solid inclusions. However, computing the microscale flow field is infeasible for practical applications as it requires detailed information about porous-medium morphology and topography which is usually unknown. Even if information on the pore structure is available, e.g. obtained from tomographic analysis [1, 2] or known in advance for artificially produced composite materials (GeoDict, www.math2market.com), performing microsca
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