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arxiv: 2604.15450 · v1 · submitted 2026-04-16 · 💻 cs.CE · physics.comp-ph· physics.geo-ph

Recognition: unknown

A shifted interface approach for internal discontinuities in poroelastic media

David Michael Riley , Guglielmo Scovazzi , Ioannis Stefanou
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Pith reviewed 2026-05-10 09:10 UTC · model grok-4.3

classification 💻 cs.CE physics.comp-phphysics.geo-ph
keywords shifted interface methodporoelasticityembedded interfacescracksBiot equationsunfitted meshesnumerical simulationdiscontinuities
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The pith

The shifted interface method can be adapted to transient poroelasticity to model embedded cracks on non-body-fitted meshes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper adapts the shifted interface method to coupled transient poroelasticity with embedded interfaces. It replaces true cracks with surrogate approximations and transfers interface conditions through local expansions for both hydraulic and mechanical fields. This allows simulation on non-body-fitted meshes without cut-cell integration or enrichment functions. Four test cases validate the approach, showing O(h) convergence of residuals away from tips, with recovery of rates by excluding tip regions. The method is demonstrated for multi-crack setups with varying properties.

Core claim

A unified derivation yields shifted forms for hydraulic transmission and mechanical traction coupling in transient poroelasticity. The true crack is replaced by a surrogate approximation where interface conditions are transferred through local expansions. Two enforcement strategies, weak integral and strong pointwise, are compared. Numerical experiments on offset mesh-aligned, boundary-intersecting angled, embedded angled, and multi-crack configurations show that interface residuals converge as O(h) away from crack tips, with first-order rates recovered when a small tip region is excluded.

What carries the argument

Shifted interface method using local expansions to transfer both hydraulic and mechanical interface conditions from true discontinuities to surrogate interfaces.

Load-bearing premise

Local expansions remain accurate for transferring coupled hydraulic and mechanical interface conditions near crack tips and in transient regimes.

What would settle it

Numerical results from an embedded angled crack test showing interface residuals that fail to converge at O(h) even after excluding a small region around the tip would indicate the claim does not hold.

Figures

Figures reproduced from arXiv: 2604.15450 by David Michael Riley, Guglielmo Scovazzi, Ioannis Stefanou.

Figure 1
Figure 1. Figure 1: Two-sided notation on the embedded interface Γ𝑐 . The interface is viewed from its two faces, Γ ± 𝑐 , with unit normals ̂𝑛 ± 𝑖 . The one-sided normal fluxes are ̂𝑞 ± 𝑖 ̂𝑛 ± 𝑖 and the one-sided tractions are 𝑡̂ ± 𝑖 = ̂𝜎 ± 𝑖𝑗 ̂𝑛 ± 𝑗 ; quantities on the (+) side are shown in green and those on the (−) side in purple [PITH_FULL_IMAGE:figures/full_fig_p021_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Computational mesh and two-sided notation. (a) The physical interface Γ𝑐 (red) is approximated by a mesh-aligned surrogate Γ̃ 𝑐 (blue) composed of faces  ℎ 𝑐 ⊂  ℎ 𝑖 ; the remaining interior faces are  ℎ 𝑖,◦ and boundary faces are  ℎ 𝜕 . (b) On an interior face 𝑒 shared by elements 𝐾− and 𝐾+ , a unit normal ̃𝑛𝑖 is fixed from 𝐾− to 𝐾+ , defining one-sided traces 𝜙 ± = 𝜙|𝐾± and the jump/average operators … view at source ↗
Figure 3
Figure 3. Figure 3: Shifted-interface geometry near the surrogate. For each point ̃𝑥 ∈ Γ̃ 𝑐 , the closest-point projection ̂𝑥 = Πℎ (̃𝑥) ∈ Γ𝑐 defines the gap vector Δ𝑖 (̃𝑥) = ̂𝑥𝑖 − ̃𝑥𝑖 . By the nearest-point property, Δ𝑖 is normal to Γ𝑐 at ̂𝑥 (right-angle marker), hence Δ𝑖 is parallel to the true normal ̂𝑛𝑖 . −0.4 −0.2 0.0 0.2 0.4 x (km) −0.4 −0.2 0.0 0.2 0.4 y (km) Ω ∂Ω˜ Γc Source −0.4 −0.2 0.0 0.2 0.4 x (km) −0.4 −0.2 0.0 0.… view at source ↗
Figure 4
Figure 4. Figure 4: Mesh-aligned offset crack configuration. The crack is offset laterally by roughly half an element width, so that the surrogate interface lies on an interior column of element faces rather than on the domain midline. D. M. Riley, G. Scovazzi, I. Stefanou Page 20 of 50 [PITH_FULL_IMAGE:figures/full_fig_p022_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Computed solution fields on the finest mesh (𝑛 = 320) for the offset crack, displayed on the deformed configuration (displacement ×104 ): (a) pore pressure 𝑝 with Darcy flux vectors, (b) mean effective stress 𝑝 𝑒 = 1 3 𝜎 𝑒 𝑘𝑘, (c) deviatoric stress invariant √ 𝐽2 , and (d) displacement magnitude ‖𝐮‖. The crack is indicated by the white line. 0.0 0.2 0.4 0.6 0.8 1.0 s 0.0 0.5 1.0 1.5 2.0 r (k m/hr) 1e−8 (a)… view at source ↗
Figure 6
Figure 6. Figure 6: Flow interface residuals along the offset crack (𝑛 = 320): (a) constitutive residual 𝑟 𝖩 = {{̂𝑞𝑗 }} ̂𝑛𝑗 − 𝖩Γ and (b) flux balance residual 𝑟 [[𝑞]] = [[ ̂𝑞𝑗 ]] ̂𝑛𝑗 . Both enforcement strategies are overlaid (indistinguishable). Residuals here are post-processed diagnostic quantities, while the residuals of the strong enforcement are zero (as shown in fig. 8). D. M. Riley, G. Scovazzi, I. Stefanou Page 21 of… view at source ↗
Figure 7
Figure 7. Figure 7: Mechanical interface residuals along the offset crack (𝑛 = 320): (a) 𝑟 [[𝑡]] 𝑖 ̂𝑛𝑖 , (b) 𝑟 [[𝑡]] 𝑖 ̂𝑚𝑖 , (c) 𝑟 𝖳 𝑖 ̂𝑛𝑖 , (d) 𝑟 𝖳 𝑖 ̂𝑚𝑖 . Residuals here are post-processed diagnostic quantities, while the residuals of the strong enforcement are zero (as shown in fig. 9). 0.0 0.2 0.4 0.6 0.8 1.0 s −0.04 −0.02 0.00 0.02 0.04 rλq (k m/hr) (a) 0.0 0.2 0.4 0.6 0.8 1.0 s −0.04 −0.02 0.00 0.02 0.04 r [[q]] λq (k m… view at source ↗
Figure 8
Figure 8. Figure 8: Flow constitutive residuals for the strong enforcement on the offset crack (𝑛 = 320): (a) 𝑟 𝖩 𝜆𝑞 and (b) 𝑟 [[𝑞]] 𝜆𝑞 . Both residuals are identically zero (to machine precision), confirming exact algebraic satisfaction of the Robin flux law. D. M. Riley, G. Scovazzi, I. Stefanou Page 22 of 50 [PITH_FULL_IMAGE:figures/full_fig_p024_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Mechanical constitutive residuals for the strong enforcement on the offset crack (𝑛 = 320): (a) 𝑟 [[𝑡]] 𝜆𝑡 ,𝑖 ̂𝑛𝑖 , (b) 𝑟 [[𝑡]] 𝜆𝑡 ,𝑖 ̂𝑚𝑖 , (c) 𝑟 𝖳 𝜆𝑡 ,𝑖 ̂𝑛𝑖 , (d) 𝑟 𝖳 𝜆𝑡 ,𝑖 ̂𝑚𝑖 . All components are identically zero, confirming exact algebraic satisfaction of the spring traction law. D. M. Riley, G. Scovazzi, I. Stefanou Page 23 of 50 [PITH_FULL_IMAGE:figures/full_fig_p025_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Convergence of interface residual norms for the mesh-aligned offset crack: (a) ‖𝑟 𝖩‖𝐿2 , (b) ‖𝑟 [[𝑞]]‖𝐿2 , (c) ‖𝑟 [[𝑡]] 𝑖 ̂𝑛𝑖‖𝐿2 , (d) ‖𝑟 [[𝑡]] 𝑖 ̂𝑚𝑖‖𝐿2 , (e) ‖𝑟 𝖳 𝑖 ̂𝑛𝑖‖𝐿2 , (f) ‖𝑟 𝖳 𝑖 ̂𝑚𝑖‖𝐿2 . The solid gray line indicates (ℎ). The strong formulation satisfies the constitutive laws pointwise; errors stem from post-processing. −0.4 −0.2 0.0 0.2 0.4 x (km) −0.4 −0.2 0.0 0.2 0.4 y (km) Ω ∂Ω˜ Γc Source −0.… view at source ↗
Figure 11
Figure 11. Figure 11: Angled crack configuration (𝜃 = arctan(0.6) ≈ 30.96◦ ). (a) Domain geometry: the crack Γ𝑐 (red) is rotated by arctan(0.6) from the horizontal. The point fluid source (purple star) is at (−0.25, −0.25). (b) Element classification on a coarse mesh: the surrogate interface Γ̃ 𝑐 (blue staircase) approximates the true crack Γ𝑐 (red) by splitting connectivity along the nearest column of element faces. Elements … view at source ↗
Figure 12
Figure 12. Figure 12: Computed solution fields on the finest mesh (𝑛 = 320) for the angled crack with 𝜃 = arctan(0.6), displayed on the deformed configuration (displacement ×104 ): (a) pore pressure 𝑝 with Darcy flux vectors, (b) mean effective stress 𝑝 𝑒 = 1 3 𝜎 𝑒 𝑘𝑘, (c) deviatoric stress invariant √ 𝐽2 , and (d) displacement magnitude ‖𝐮‖. 0.0 0.2 0.4 0.6 0.8 1.0 s −1.4 −1.2 −1.0 −0.8 −0.6 −0.4 −0.2 0.0 r (k m/hr) 1e−6 (a) … view at source ↗
Figure 13
Figure 13. Figure 13: Flow interface residuals along the angled crack with 𝜃 = arctan(0.6) (𝑛 = 320): (a) constitutive residual 𝑟 𝖩 = {{̂𝑞𝑗 }} ̂𝑛𝑗 −𝖩Γ , and (b) flux balance residual 𝑟 [[𝑞]] = [[ ̂𝑞𝑗 ]] ̂𝑛𝑗 . Both enforcement strategies are overlaid. The strong formulation satisfies the constitutive laws pointwise; errors stem from post-processing. D. M. Riley, G. Scovazzi, I. Stefanou Page 25 of 50 [PITH_FULL_IMAGE:figures/f… view at source ↗
Figure 14
Figure 14. Figure 14: Mechanical interface residuals along the angled crack with 𝜃 = arctan(0.6) (𝑛 = 320): (a) 𝑟 [[𝑡]] 𝑖 ̂𝑛𝑖 (normal traction balance), (b) 𝑟 [[𝑡]] 𝑖 ̂𝑚𝑖 (tangential traction balance), (c) 𝑟 𝖳 𝑖 ̂𝑛𝑖 (normal constitutive residual), (d) 𝑟 𝖳 𝑖 ̂𝑚𝑖 (tangential constitutive residual). Both enforcement strategies are overlaid. The strong formulation satisfies the constitutive laws pointwise; errors stem from post-pr… view at source ↗
Figure 15
Figure 15. Figure 15: Convergence of interface residual norms for the angled crack with 𝜃 = arctan(0.6): (a) ‖𝑟 𝖩‖𝐿2 , (b) ‖𝑟 [[𝑞]]‖𝐿2 , (c) ‖𝑟 [[𝑡]] 𝑖 ̂𝑛𝑖‖𝐿2 , (d) ‖𝑟 [[𝑡]] 𝑖 ̂𝑚𝑖‖𝐿2 , (e) ‖𝑟 𝖳 𝑖 ̂𝑛𝑖‖𝐿2 , (f) ‖𝑟 𝖳 𝑖 ̂𝑚𝑖‖𝐿2 . The solid gray line indicates (ℎ). The strong formulation satisfies the constitutive laws pointwise; errors stem from post-processing. D. M. Riley, G. Scovazzi, I. Stefanou Page 27 of 50 [PITH_FULL_IMAGE… view at source ↗
Figure 16
Figure 16. Figure 16: Effect of tip trimming on the convergence of interface residual norms for the angled crack with 𝜃 = arctan(0.6). Each curve corresponds to excluding a percentage 𝜖 of the crack length at each tip before computing the 𝐿2 norm. Left column: weak enforcement; right column: strong enforcement. Rows from top to bottom: (a,b) ‖𝑟 𝖩‖𝐿2 , (c,d) ‖𝑟 [[𝑞]]‖𝐿2 , (e,f) ‖𝑟 [[𝑡]] 𝑖 ̂𝑛𝑖‖𝐿2 , (g,h) ‖𝑟 [[𝑡]] 𝑖 ̂𝑚𝑖‖𝐿2 , (i,j… view at source ↗
Figure 17
Figure 17. Figure 17: Bulk-field 𝐿2 (Ω) self-convergence for the angled crack with 𝜃 = arctan(0.6). Each plotted point shows the relative error eq. (66) for one adjacent-level comparison: 𝑛 = 20 against 40, 40 against 80, 80 against 160, and 160 against 320. (a) Pressure, (b) displacement. The gray 𝑂(ℎ) and 𝑂(ℎ 4∕3) lines are shown only as visual references. In particular, the 𝑂(ℎ 4∕3) guide is motivated by reduced-regularity … view at source ↗
Figure 18
Figure 18. Figure 18: Embedded angled crack configuration (𝜃 = arctan(0.6) ≈ 30.96◦ , 𝐿𝑐 = 1 2 √ 1 + 0.6 2 ≈ 0.583 km). (a) Domain geometry: the crack Γ𝑐 (red) is rotated by arctan(0.6) from the horizontal with both tips in the domain interior. The point fluid source (purple star) is at (−0.25, −0.25). (b) Element classification on a coarse mesh: the surrogate interface Γ̃ 𝑐 (blue staircase) approximates the true crack Γ𝑐 (red… view at source ↗
Figure 19
Figure 19. Figure 19: Computed solution fields on the finest mesh (𝑛 = 320) for the embedded angled crack with 𝜃 = arctan(0.6), displayed on the deformed configuration (displacement ×104 ): (a) pore pressure 𝑝 with Darcy flux vectors, (b) mean effective stress 𝑝 𝑒 = 1 3 𝜎 𝑒 𝑘𝑘, (c) deviatoric stress invariant √ 𝐽2 , and (d) displacement magnitude ‖𝐮‖. D. M. Riley, G. Scovazzi, I. Stefanou Page 33 of 50 [PITH_FULL_IMAGE:figure… view at source ↗
Figure 20
Figure 20. Figure 20: Flow interface residuals along the embedded angled crack with 𝜃 = arctan(0.6) (𝑛 = 320): (a) constitutive residual 𝑟 𝖩 = {{̂𝑞𝑗 }} ̂𝑛𝑗 − 𝖩Γ , and (b) flux balance residual 𝑟 [[𝑞]] = [[ ̂𝑞𝑗 ]] ̂𝑛𝑗 . Sharp spikes appear at both crack tips, reflecting the interior tip artifact. Both enforcement strategies are overlaid. The strong formulation satisfies the constitutive laws pointwise; errors stem from post-pro… view at source ↗
Figure 21
Figure 21. Figure 21: Mechanical interface residuals along the embedded angled crack with 𝜃 = arctan(0.6) (𝑛 = 320): (a) 𝑟 [[𝑡]] 𝑖 ̂𝑛𝑖 (normal traction balance), (b) 𝑟 [[𝑡]] 𝑖 ̂𝑚𝑖 (tangential traction balance), (c) 𝑟 𝖳 𝑖 ̂𝑛𝑖 (normal constitutive residual), (d) 𝑟 𝖳 𝑖 ̂𝑚𝑖 (tangential constitutive residual). The strong formulation satisfies the constitutive laws pointwise; errors stem from post-processing. D. M. Riley, G. Scovazz… view at source ↗
Figure 22
Figure 22. Figure 22: Convergence of interface residual norms for the embedded angled crack with 𝜃 = arctan(0.6): (a) ‖𝑟 𝖩‖𝐿2 , (b) ‖𝑟 [[𝑞]]‖𝐿2 , (c) ‖𝑟 [[𝑡]] 𝑖 ̂𝑛𝑖‖𝐿2 , (d) ‖𝑟 [[𝑡]] 𝑖 ̂𝑚𝑖‖𝐿2 , (e) ‖𝑟 𝖳 𝑖 ̂𝑛𝑖‖𝐿2 , (f) ‖𝑟 𝖳 𝑖 ̂𝑚𝑖‖𝐿2 . The solid gray line indicates (ℎ). The strong formulation satisfies the constitutive laws pointwise; errors stem from post-processing. D. M. Riley, G. Scovazzi, I. Stefanou Page 38 of 50 [PITH_F… view at source ↗
Figure 23
Figure 23. Figure 23: Effect of tip trimming on the convergence of interface residual norms for the embedded angled crack with 𝜃 = arctan(0.6). Each curve corresponds to excluding a percentage 𝜖 of the crack length at each tip before computing the 𝐿2 norm. Left column: weak enforcement; right column: strong enforcement. Rows from top to bottom: (a,b) ‖𝑟 𝖩‖𝐿2 , (c,d) ‖𝑟 [[𝑞]]‖𝐿2 , (e,f) ‖𝑟 [[𝑡]] 𝑖 ̂𝑛𝑖‖𝐿2 , (g,h) ‖𝑟 [[𝑡]] 𝑖 ̂𝑚𝑖‖… view at source ↗
Figure 24
Figure 24. Figure 24: Bulk-field 𝐿2 (Ω) self-convergence for the embedded angled crack with 𝜃 = arctan(0.6). Format as in fig. 17. D. M. Riley, G. Scovazzi, I. Stefanou Page 40 of 50 [PITH_FULL_IMAGE:figures/full_fig_p042_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: One-sided interface quantities on the finest mesh (𝑛 = 320) for the embedded crack with 𝜃 = arctan(0.6): body￾fitted mesh (left column) versus shifted interface method (right column). Rows: (a,b) normal flux 𝑞𝑛 , (c,d) normal traction 𝜎𝑛𝑛, (e,f) tangential traction 𝜎𝑛𝑡. Filled circles show the weak-enforcement post-processed traces ((+), green; (−), purple); open squares show the strong-enforcement interf… view at source ↗
Figure 26
Figure 26. Figure 26: Multi-crack configuration. (a) Domain geometry showing the four cracks: a C-shaped polyline Γ𝑐0 (red), an oblique straight line Γ𝑐1 (green), a smooth S-curve Γ𝑐2 (orange), and a parabolic arc Γ𝑐3 (purple). The injection (green star) and extraction (purple star) wells are indicated. (b) Element classification on a coarse mesh: the surrogate interfaces Γ̃ 𝑐 (blue staircase segments) approximate the true cra… view at source ↗
Figure 27
Figure 27. Figure 27: Computed solution fields on the 𝑛 = 160 mesh for the multi-crack configuration, displayed on the deformed configuration (displacement ×104 ): (a) pore pressure 𝑝 with Darcy flux streamlines, (b) mean effective stress 𝑝 𝑒 = 1 3 𝜎 𝑒 𝑘𝑘, (c) deviatoric stress invariant √ 𝐽2 , and (d) displacement magnitude ‖𝐮‖. The four cracks are visible as olive colored traces. The interaction between the injection–extract… view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript adapts the shifted interface method to transient poroelasticity with embedded discontinuities. It replaces true cracks with surrogate interfaces, derives unified shifted forms for hydraulic (pressure/flux) and mechanical (traction/displacement) transmission conditions via local expansions, and compares weak integral versus strong pointwise enforcement. Validation on four test cases of increasing complexity (offset mesh-aligned, boundary-intersecting angled, embedded angled, and multi-crack) shows interface residuals converging as O(h) away from crack tips, with first-order rates recovered when tip regions are excluded. A multi-crack demonstration with distinct geometries and properties supports applicability to complex embedded interfaces on non-body-fitted meshes.

Significance. If the local expansions remain accurate for the coupled Biot system, the work supplies a practical alternative to body-fitted meshing or enrichment techniques for poroelastic crack problems in geomechanics and biomechanics. Strengths include the unified derivation for both flow and mechanics, direct comparison of enforcement strategies, manufactured-solution validation across geometrically varied cases, and explicit acknowledgment of tip-region degradation with recovery upon exclusion. These elements position the framework as mesh-flexible for complex discontinuities.

major comments (1)
  1. Abstract: The reported O(h) convergence of interface residuals is measured away from crack tips, with first-order rates recovered only after excluding a small tip region. For the tightly coupled Biot system, where displacement and pressure gradients are singular at tips and linked through storage and Darcy terms, the local expansions used to transfer the true jump conditions to the surrogate interface may introduce non-uniform errors when the distance to the tip is O(h). Additional analysis or tests (e.g., transient loading with quantified residuals inside the singular zone) are needed to confirm consistency of the transferred conditions, as this directly supports the central claim of a practical framework for poroelastic crack modeling.
minor comments (2)
  1. The abstract and results section would benefit from explicit statement of the Taylor expansion order employed in the local expansions for both hydraulic and mechanical conditions.
  2. Include quantitative error tables (with exact rates and L2/H1 norms) for the four test cases alongside convergence plots to permit direct assessment of the claimed O(h) behavior away from tips.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of the manuscript and the recommendation for minor revision. We provide a detailed response to the major comment below.

read point-by-point responses

  1. Referee: Abstract: The reported O(h) convergence of interface residuals is measured away from crack tips, with first-order rates recovered only after excluding a small tip region. For the tightly coupled Biot system, where displacement and pressure gradients are singular at tips and linked through storage and Darcy terms, the local expansions used to transfer the true jump conditions to the surrogate interface may introduce non-uniform errors when the distance to the tip is O(h). Additional analysis or tests (e.g., transient loading with quantified residuals inside the singular zone) are needed to confirm consistency of the transferred conditions, as this directly supports the central claim of a practical framework for poroelastic crack modeling.

    Authors: We thank the referee for this insightful comment on the behavior near crack tips. The manuscript already reports that interface residuals converge as O(h) away from crack tips, with first-order rates recovered upon exclusion of a small tip region; this is explicitly stated in the abstract and demonstrated across the four test cases. The local expansions rely on Taylor series that assume local smoothness, and their accuracy necessarily degrades within O(h) of the tip because the Biot solution fields (displacements and pressures) are singular there due to the storage and Darcy coupling terms. This singularity is a physical feature of the problem and would affect the local accuracy of any unfitted or body-fitted discretization that does not employ dedicated tip enrichment. The consistency of the shifted transmission conditions is confirmed by the clean O(h) convergence obtained on the smooth portions of the interfaces in all geometries considered, including configurations with transient poroelastic loading. We therefore view the existing validation as sufficient to support the central claim of a practical framework for embedded discontinuities on unfitted meshes. No additional tests inside the singular zone are required, as they would simply reproduce the expected degradation already documented. revision: no

Circularity Check

0 steps flagged

Derivation is self-contained from Biot equations with no circular reductions

full rationale

The paper presents a unified derivation of shifted hydraulic and mechanical interface conditions directly from the Biot poroelastic equations and standard transmission conditions at discontinuities, using local Taylor expansions to transfer jumps to a surrogate interface. Validation relies on manufactured solutions and convergence studies rather than parameter fitting to target outputs. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations that collapse the central claim to its own inputs are present in the provided derivation chain. The adaptation of the shifted interface method supplies an independent starting point whose extension to transient coupled poroelasticity is explicitly constructed from first principles.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard Biot poroelasticity and finite-element assumptions; no new free parameters, invented entities, or ad-hoc constants are introduced.

axioms (2)
  • domain assumption Linear Biot theory governs the coupled hydromechanical response in the porous medium.
    Invoked throughout the abstract as the governing equations for pressure-displacement coupling.
  • ad hoc to paper Local expansions around the surrogate interface accurately transmit the true crack conditions for both flow and traction.
    Core modeling assumption of the shifted interface approach; its validity is tested numerically but not proven a priori.

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