arXiv subjects

Elissa Eggenweiler

Publications and source records attributed to Elissa Eggenweiler.

6 recordsLinked to original sources

arXiv2025

Higher-order coupling conditions for arbitrary flows in Stokes-Darcy systems

The choice of interface conditions for coupling free-flow and porous-medium flow systems is crucial in order to obtain accurate coupled flow models and precise numerical simulation results. Typically, the Stokes equations are considered in the free-flow region, Darcy's law is applied in the porous medium, and traditional coupling conditions (conservation of mass, balance of normal forces, the Beavers-Joseph condition on tangential velocity) are set on the interface. However, these traditional conditions are applicable to flows parallel to the fluid-porous interface only. Recently, we derived generalized interface conditions accounting for arbitrary flow directions to the porous layer using homogenization and boundary layer theory. We validated these conditions numerically and demonstrated that they are more accurate than the traditional coupling conditions. However, error estimates have not been derived yet. In this paper, we extend the generalized coupling conditions and prove rigorous error estimates for the homogenization result. All effective parameters appearing in the developed higher-order interface conditions are computed numerically based on the pore geometry. We validate the derived conditions by comparing numerical simulation results for the coupled Stokes-Darcy model and the pore-scale resolved model. Moreover, we compare the new coupling conditions to the traditional as well as generalized interface conditions and highlight the importance of the additional higher-order terms appearing in the derived coupling concept.

math.AP↗

arXiv2022

A Surrogate-Assisted Uncertainty-Aware Bayesian Validation Framework and its Application to Coupling Free Flow and Porous-Medium Flow

Existing model validation studies in geoscience often disregard or partly account for uncertainties in observations, model choices, and input parameters. In this work, we develop a statistical framework that incorporates a probabilistic modeling technique using a fully Bayesian approach to perform a quantitative uncertainty-aware validation. A Bayesian perspective on a validation task yields an optimal bias-variance trade-off against the reference data. It provides an integrative metric for model validation that incorporates parameter and conceptual uncertainty. Additionally, a surrogate modeling technique, namely Bayesian Sparse Polynomial Chaos Expansion, is employed to accelerate the computationally demanding Bayesian calibration and validation. We apply this validation framework to perform a comparative evaluation of models for coupling a free flow with a porous-medium flow. The correct choice of interface conditions and proper model parameters for such coupled flow systems is crucial for physically consistent modeling and accurate numerical simulations of applications. We develop a benchmark scenario that uses the Stokes equations to describe the free flow and considers different models for the porous-medium compartment and the coupling at the fluid--porous interface. These models include a porous-medium model using Darcy's law at the representative elementary volume scale with classical or generalized interface conditions and a pore-network model with its related coupling approach. We study the coupled flow problems' behaviors considering a benchmark case, where a pore-scale resolved model provides the reference solution. With the suggested framework, we perform sensitivity analysis, quantify the parametric uncertainties, demonstrate each model's predictive capabilities, and make a probabilistic model comparison.

stat.AP↗

arXiv2022

A modification of the Beavers-Joseph condition for arbitrary flows to the fluid-porous interface

Physically consistent coupling conditions at the fluid-porous interface with correctly determined effective parameters are necessary for accurate modeling and simulation of various applications. To describe single-fluid-phase flows in coupled free-flow and porous-medium systems, the Stokes/Darcy equations are typically used together with the conservation of mass across the interface, the balance of normal forces and the Beavers-Joseph condition on the tangential velocity. The latter condition is suitable for flows parallel to the interface but not applicable for arbitrary flow directions. Moreover, the value of the Beavers-Joseph slip coefficient is uncertain. In the literature, it is routinely set equal to one that is not correct for many applications, even if the flow is parallel to the porous layer. In this paper, we reformulate the generalized interface condition on the tangential velocity component, recently developed for arbitrary flows in Stokes/Darcy systems, such that it has the same analytical form as the Beavers-Joseph condition. We compute the effective coefficients appearing in this modified condition using theory of homogenization with boundary layers. We demonstrate that the modified Beavers-Joseph condition is applicable for arbitrary flow directions to the fluid-porous interface. In addition, we propose an efficient two-level numerical algorithm based on simulated annealing to compute the optimal Beavers-Joseph parameter.

physics.flu-dyn↗

arXiv2021

Analysis of the Stokes-Darcy problem with generalised interface conditions

Fluid flows in coupled systems consisting of a free-flow region and the adjacent porous medium appear in a variety of environmental settings and industrial applications. In many applications, fluid flow is non-parallel to the fluid-porous interface that requires a generalisation of the Beavers-Joseph coupling condition typically used for the Stokes-Darcy problem. Generalised coupling conditions valid for arbitrary flow directions to the interface are recently derived using the theory of homogenisation and boundary layers. The aim of this work is the mathematical analysis of the Stokes-Darcy problem with these generalised interface conditions. We prove the existence and uniqueness of the weak solution of the coupled problem. The well-posedness is guaranteed under a suitable relationship between the permeability and the boundary layer constants containing geometrical information about the porous medium and the interface. We numerically study the validity of the obtained results for realistic problems and provide a benchmark for numerical solution of the Stokes-Darcy problem with generalised interface conditions.

math.AP↗

arXiv2020

Effective coupling conditions for arbitrary flows in Stokes-Darcy systems

Boundary conditions at the interface between the free-flow region and the adjacent porous medium is a key issue for physically consistent modeling and accurate numerical simulation of flow and transport processes in coupled systems due to the interface driven nature of such processes. Interface conditions available in the literature have several weak points: most of them are suitable only for flows parallel to the fluid-porous interface, some are restricted to specific boundary value problems, and others contain unknown model parameters which still need to be determined. These facts severely restrict the variety of applications that can be successfully modeled. We propose new interface conditions which are valid for arbitrary flow directions. These coupling conditions are rigorously derived using the theory of homogenization and boundary layers. All effective parameters appearing in these conditions are computed numerically based on the geometrical configuration of the coupled system. The developed conditions are validated by comparison of numerical simulation results for the coupled Stokes-Darcy model and the pore-scale resolved model. In addition, the new interface conditions are compared with the classical conditions to demonstrate the advantage of the proposed conditions.

math.NA↗

arXiv2019

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

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.

math.NA↗