Uncertainty-aware Validation Benchmarks for Coupling Free Flow and Porous-Medium Flow

The correct choice of interface conditions and proper model parameters for coupled free-flow and porous-medium systems is vital for physically consistent modeling and accurate numerical simulations of applications. We apply the Stokes equations to describe the free flow and consider different models for both the porous-medium compartment and the coupling at the fluid--porous interface. These models are the REV-scale porous-medium model in the form of Darcy's law with classical or generalized interface conditions and the 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, and quantify the uncertainties in the models' parameters and the reference data. For this purpose, we apply a statistical framework that incorporates a probabilistic modeling technique using a fully Bayesian approach. 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 model reduction technique, namely Bayesian Sparse Polynomial Chaos Expansion, is employed to accelerate the calibration and validation processes for the computationally demanding free-flow and porous-medium models using different coupling strategies. We perform uncertainty-aware validation, demonstrate each model's predictive capabilities, and make a probabilistic model comparison using a Bayesian validation metric.