Shape factors for irregular apertures via high-order polynomial reconstruction and a Galerkin-based integral formulation

Resumo

This study presents a Galerkin-based integral (GBI) method for computing shape factors in cross-sections bounded by irregular geometries, as commonly found in fractured systems. The approach combines high-order piecewise polynomial reconstruction of the aperture boundary with a semi-analytical formulation based on weighted residuals to solve the governing flow equations under laminar conditions. A set of three realistic geometries, obtained from fractures in cylindrical concrete specimens, was used to evaluate the method’s performance. Results include velocity fields, Poiseuille numbers, and shape factors, all computed with high accuracy and low computational cost. Validation against finite element solutions implemented in FEniCSx/DolfinX shows excellent agreement across all tested cases, confirming the robustness and precision of the GBI method. Despite minor discontinuities at subdomain interfaces, the computed hydraulic quantities remain consistent and reliable. The proposed methodology offers a computationally efficient alternative to traditional discretization techniques for modeling transport phenomena in porous or fractured media.