A shifted interface approach for internal discontinuities in poroelastic media

2026-04-16

AI Summary

This work addresses transient poroelastic problems involving fractures or multiphase interfaces, where traditional body-fitted meshes are computationally expensive and unfitted approaches often require intricate integration schemes or stabilization techniques. For the first time, the shifted interface method is extended to the Biot poroelasticity framework, enabling the transfer of exact interface conditions to an approximate interface via local Taylor expansions on unfitted meshes. This approach uniformly handles hydromechanical coupling and systematically compares weak (integral) and strong (pointwise) constraint strategies. Notably, it avoids cut-cell integration or enrichment functions, allowing efficient simulation of geometrically complex embedded fracture networks. Numerical experiments demonstrate first-order convergence of interface residuals—excluding small regions near crack tips—and successfully validate the method in a scenario featuring four heterogeneous fractures.

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Abstract

Porous media containing cracks, fractures, or internal discontinuities arise throughout subsurface geomechanics, biomechanics, and materials science. Numerical simulation of the coupled hydromechanical response is inherently challenging because the pressure and displacement fields are tightly coupled through the Biot equations, requiring stable mixed formulations. These difficulties are compounded when cracks are present, because standard mesh-conforming approaches require costly, labor-intensive, body-fitted meshing, while unfitted methods often require cut-cell integration, enrichment functions, or additional stabilization. In this work, we use an alternative approach, we adapt the shifted interface method to coupled transient poroelasticity with embedded interfaces. The method replaces the true crack by a surrogate approximation where interface conditions are transferred through local expansions. A unified derivation yields shifted forms for both hydraulic transmission and mechanical traction coupling. Two enforcement strategies are extensively compared: a weak (integral) enforcement and a strong (pointwise) enforcement. Four test cases of increasing geometric complexity (offset mesh-aligned, boundary-intersecting angled, embedded angled, and multi-crack configurations) validate the formulation. Away from crack tips, interface residuals converge as O(h); near tips, localized post-processing artifacts degrade the global rate, but first-order convergence is recovered when a small tip region is excluded. A multi-crack demonstration with four simultaneously embedded cracks of distinct geometry and interface properties confirms the practical applicability of the framework. These results support the shifted interface method as a practical framework for poroelastic crack modeling on non-body-fitted meshes with geometrically complex embedded interfaces.

Problem

• poroelasticity
• internal discontinuities
• cracks
• hydromechanical coupling
• non-body-fitted meshes

Innovation

• shifted interface method
• poroelasticity
• embedded interfaces
• non-body-fitted meshes
• hydromechanical coupling