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

A correct choice of interface conditions and useful model parameters for coupled free-flow and porous-medium systems is vital for physically consistent modeling and accurate numerical simulations of applications. We consider the Stokes--Darcy problem with different models for the porous-medium compartment and corresponding coupling strategies: the standard averaged model based on Darcy's law with classical or generalized interface conditions, as well as the pore-network model. 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. To achieve this, 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 computationally demanding Stokes--Darcy models with different coupling strategies. We perform uncertainty-aware validation, demonstrate each model's predictive capabilities, and make a model comparison using a Bayesian validation metric.