Calibration of stress-jump conditions for arbitrary flow directions in fluid-porous systems

TL;DR

This paper validates and calibrates stress-jump conditions for Stokes-Darcy flow in 2D, demonstrating that a simplified parameter calibration can effectively model flow across porous and free-flow regions.

Contribution

It provides a calibration method for stress-jump parameters in arbitrary flow directions, reducing complexity while maintaining accuracy.

Findings

Effective one-dimensional calibration reduces parameter complexity.

Robustness of the model with coarse parameter estimates.

Validation shows negligible accuracy loss with simplified calibration.

Abstract

A numerical validation of the stress-jump coupling conditions for Stokes-Darcy flow in two dimensions is presented, addressing a gap that has remained since their introduction by Angot et al.. These conditions, formulated for arbitrary flow directions at the interface between a porous medium and an adjacent free-flow region, involve a friction tensor whose coefficients are not known a priori. We calibrate these parameters for a range of porous-medium configurations and flow regimes by matching the macroscopic model to reference solutions derived from processed pore-scale simulations. Several optimization strategies are assessed for this calibration task. The results show that, although three parameters are formally required, exploiting structural properties of the porous medium enables an effective reduction to a one-dimensional calibration with negligible loss in accuracy. A regional sensitivity analysis further indicates that even coarse parameter estimates can yield a well-performing model, highlighting the robustness and practical applicability of the stress-jump formulation.