{"id":"a62f7db0-3faf-4d84-bbef-68ec681ee2e1","arxiv_id":"2607.07432","paper_version":1,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":3,"one_line_summary":"A target-value reconstruction strategy corrects the inward displacement of the effective boundary in fully one-sided diffuse-interface immersed boundary methods, reducing no-slip and isothermal errors by 77% and 85%.","lead":"The paper fixes a systematic inward shift of the effective boundary in one-sided diffuse-interface immersed boundary methods by reconstructing target values at a virtual point. This improves accuracy for compressible flow simulations around complex geometries on Cartesian grids.","discovery_kind":"unclear","skeptic_critique":{"model":"glm-5.2","headline":"The linear reconstruction at the virtual point relies on flow variables sampled inside the IBM forcing layer, where values are not independently physical; sensitivity of this to wall-normal gradient strength is untested.","rationale":"The reader's weakest_assumption identifies the linear interpolation concern, which is directionally correct. However, the more precise load-bearing issue is that M_P* is sampled from within the IBM forcing layer, making the gradient estimate dependent on forcing convergence — not merely on geometric curvature or gradient strength. This is a subtler and more fundamental version of the reader's concern. Despite this, the paper's validation across multiple geometries (cylinder, star, NACA0012, sphere) and flow regimes (subsonic to supersonic, steady and unsteady) provides reasonable evidence that the method is robust in practice. The error reductions are well-documented, the method is clearly described, and the computational cost is genuinely negligible. The 8% Neumann error increase is honestly reported and explained (the reconstruction reduces to M_V^t = M_P* for zero-gradient conditions, which is essentially the same as the original FODIBM). No code or data is shipped, which limits independent verification, but the methods are specified with sufficient detail for reproduction. The ACCEPT verdict with MODERATE confidence is appropriate — the contribution is real and well-executed, but the untested regimes (strong wall-normal gradients, very high curvature, shock-boundary interactions) leave some residual uncertainty about the generality of the error reduction claims.","tokens_in":22078,"tokens_out":4828,"duration_ms":256288,"concrete_test":"Run the supersonic cylinder case (Ma=2, Re=300) with a strong wall-normal temperature gradient by switching from adiabatic to a cold-wall isothermal condition (T_wall << T_∞) and compare the FODIBM-R boundary-condition error and near-wall temperature profile against a body-fitted reference. If the isothermal error reduction remains comparable to the reported 85% and the near-wall profile matches the body-fitted solution within the same tolerance as the current cases, the reconstruction is robust to strong gradients. If the error reduction degrades significantly (e.g., drops below 50%), the linear interpolation using forced-region values is a limiting assumption.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The reader correctly identifies the linear interpolation assumption (Eqs. 26–27) as a potential weak point, but the more specific concern is about the source of M_P*. The projection point P sits at d_n = 1.5Δx inside the body, within the IBM forcing layer (delta function support radius d=2). The value M_P* is obtained by interpolating from Eulerian points that are themselves influenced by the IBM forcing from the current or previous time steps. Thus M_P* is not an independently resolved flow variable — it is a forced value whose accuracy depends on how well the forcing has already enforced the boundary condition. The reconstruction in Eq. 27 then uses the difference (M_P* − M_B^t) to estimate the near-wall gradient and extrapolate the target to the virtual point V. If the forcing has not yet converged (e.g., during transient startup, near shock-boundary interactions, or at geometric singularities where the one-sided support is poorly conditioned), M_P* could be unreliable, and the reconstructed target would propagate that error rather than correct it. The paper does not analyze the sensitivity of the reconstruction to the quality of M_P*, nor does it report results for flows with strong wall-normal gradients (e.g., high-Re boundary layers, shock-wave/boundary-layer interactions). The validation cases (Re = 200–5000, moderate Mach numbers) may not stress this regime. That said, the method is self-consistent in steady state: once the forcing converges, M_P* reflects the physical near-wall gradient, and the reconstruction is valid. The 77% and 85% error reductions and the good agreement with body-fitted solutions support this. The concern is about robustness in regimes not tested, not about a fundamental flaw.","agreement_with_reader":"partial"},"referee_report":{"model":"glm-5.2","summary":"The manuscript presents a target-value reconstruction strategy for the fully one-sided diffuse-interface immersed boundary method (FODIBM), aimed at correcting an inward displacement of the effective boundary caused by the asymmetric kernel support of the one-sided spreading operator. The authors derive the effective boundary shift analytically (Eq. 25), propose a linear reconstruction at a virtual point (Eqs. 26–29) to compensate, and demonstrate through convergence studies and 2D/3D validation cases that the correction reduces Dirichlet and isothermal boundary-condition errors by 77% and 85% respectively, at negligible computational cost. The method is coupled to a hybrid lattice Boltzmann solver and validated against body-fitted and experimental data across subsonic to supersonic regimes.","tokens_in":22922,"tokens_out":1232,"duration_ms":196095,"significance":"The central contribution — identifying and quantitatively correcting the effective boundary shift inherent to one-sided spreading — is well-motivated and addresses a genuine gap in the FODIBM framework. The boundary-shift analysis (Eq. 25) is clean and directly confirmed by the velocity profile in Fig. 3. The convergence study (Fig. 4) demonstrates approximately second-order accuracy. The validation suite is broad: 2D cylinder, star geometries, NACA0012 airfoil (three regimes), 3D sphere, and rotating sphere, all with quantitative comparisons to external reference data. The computational cost analysis (Table 3) showing <1.5% overhead is a practical strength. The reconstruction is parameter-free in the sense that the virtual-point location is determined by Eq. (25) rather than empirically tuned, which is a notable advantage over retraction-based approaches.","major_comments":[{"comment":"§3.2, Table 2: The Neumann boundary-condition error for FODIBM-R is reported as 1.10×10⁻², an 8% increase relative to FODIBM (1.02×10⁻²). The abstract states that the method 'applies to both Dirichlet and Neumann boundary conditions' and 'substantially improves boundary-condition enforcement.' However, for the Neumann case the error slightly worsens. The text in §3.2 explains this is because the reconstructed target temperature for the adiabatic case reduces to M_V^t = M_P* (Eq. 29), which is identical to the FODIBM treatment. This is internally consistent, but the abstract's claim of improvement for Neumann conditions is not supported by the data. The authors should clarify in the abstract that the improvement is specific to Dirichlet conditions, or restrict the scope of the Neumann claim.","section":null},{"comment":"§2.4, Eqs. (26)–(27): The linear reconstruction at the virtual point V uses M_P* sampled at the projection point P, which sits at d_n = 1.5Δx inside the body within the IBM forcing layer (delta function support radius d = 2). The value M_P* is obtained by interpolating from Eulerian points that are themselves influenced by IBM forcing. The manuscript does not analyze the sensitivity of the reconstruction to the quality of M_P*, particularly during transient startup, near shock-boundary interactions, or at geometric singularities (e.g., star concavities) where the one-sided support may be poorly conditioned. The validation cases (Re = 200–5000, moderate Mach numbers) may not stress this regime. A brief discussion of this limitation — or a sensitivity check on a case with strong wall-normal gradients — would strengthen the paper and clarify the applicability envelope.","section":null}],"minor_comments":[{"comment":"§2.4, Fig. 1: The schematic shows points B, V, and P, but the distances d_BV and d_PB are not labeled on the figure. Adding these labels would make Eqs. (26)–(29) immediately interpretable.","section":null},{"comment":"§3.1, Fig. 4: The L∞ convergence rate is described as 'less pronounced' than the L2 rate. A quantitative slope estimate for the L∞ data would help the reader assess whether the rate degrades below second order.","section":null},{"comment":"§3.4, Table 4: The shock stand-off distance Δs for FODIBM-R (0.71) is compared to body-fitted values of 0.73 (Ménez) and 0.70 (Takahashi). The scatter in reference data is comparable to the FODIBM-R improvement. A note on the uncertainty in reference values would contextualize the comparison.","section":null},{"comment":"§3.7, Fig. 14 caption: The description of background contours (black solid = hybrid LBM, white dashed = FODIBM-R) is clear, but the domain dimensions reference D without defining D for the airfoil case (chord c is used for Re). Clarify whether D = c here.","section":null},{"comment":"The Hermite weighting parameter τ is set to 0.98 (Appendix A, Eq. A.7) without sensitivity discussion. A brief note on whether results are sensitive to this choice would be helpful.","section":null},{"comment":"References [5] and [6] are authored by the present authors and are tangential to the IBM methodology. They could be removed or the citation list streamlined for focus.","section":null}],"recommendation":"minor_revision","confidential_remarks":"The paper builds directly on the authors' prior FODIBM framework [33], which is cited appropriately. The central contribution here (target-value reconstruction) is derived independently from the boundary-shift analysis and is not circular. The stress-test concern about M_P* being a forced rather than independently resolved value is valid but does not constitute a load-bearing error: the method is self-consistent in steady state, and the validation cases confirm this. The concern would become load-bearing only if the authors claimed the method is robust for high-Re boundary layers or shock/boundary-layer interactions, which they do not. I recommend minor revision with the two major comments addressed."},"author_rebuttal":{"model":"glm-5.2","summary":"We thank the referee for the careful reading and constructive comments. Both major points are well-taken and will be addressed in the revised manuscript.","responses":[{"response":"The referee is correct. The data in Table 2 show that the Neumann (adiabatic) boundary-condition error slightly increases from 1.02×10⁻² to 1.10×10⁻² (8%) with the reconstruction, because for zero-gradient Neumann conditions Eq. (29) reduces to M_V^t = M_P*, which is identical to the FODIBM treatment. The abstract's claim that the method 'substantially improves boundary-condition enforcement' is accurate for Dirichlet conditions (77% and 85% reductions) but is not supported for Neumann conditions. We will revise the abstract to clarify that the substantial improvement is specific to Dirichlet conditions, and that the method applies to both Dirichlet and Neumann conditions without degrading Neumann accuracy. The phrase 'substantially improves boundary-condition enforcement' will be qualified accordingly.","revision_made":"yes","referee_comment":"§3.2, Table 2: The Neumann boundary-condition error for FODIBM-R is reported as 1.10×10⁻², an 8% increase relative to FODIBM (1.02×10⁻²). The abstract states that the method 'applies to both Dirichlet and Neumann boundary conditions' and 'substantially improves boundary-condition enforcement.' However, for the Neumann case the error slightly worsens. The authors should clarify in the abstract that the improvement is specific to Dirichlet conditions, or restrict the scope of the Neumann claim."},{"response":"The referee raises a valid concern. The quality of M_P* depends on the local flow field at Eulerian points within the forcing layer, which are themselves influenced by the IBM forcing. In principle, this could degrade reconstruction accuracy in regimes with strong wall-normal gradients, during transient startup, or at geometric singularities. We note that the star geometry cases (§3.6) do exercise concavities, and the results show good agreement with body-fitted reference data, providing some indirect evidence of robustness. However, we agree that a systematic discussion of this limitation is missing. We will add a paragraph to §2.4 (or §3) discussing the sensitivity of the reconstruction to M_P* quality, noting that: (1) the linear reconstruction assumes locally linear variation of flow variables along the normal, which may be violated near shocks or at singularities; (2) the validation cases presented (Re = 200–5000, moderate Mach numbers) do not stress extreme wall-normal gradients; and (3) the method's applicability envelope in such regimes remains to be fully characterized. We will also note this as a direction for future investigation.","revision_made":"yes","referee_comment":"§2.4, Eqs. (26)–(27): The linear reconstruction at the virtual point V uses M_P* sampled at the projection point P, which sits at d_n = 1.5Δx inside the body within the IBM forcing layer. The value M_P* is obtained by interpolating from Eulerian points that are themselves influenced by IBM forcing. The manuscript does not analyze the sensitivity of the reconstruction to the quality of M_P*, particularly during transient startup, near shock-boundary interactions, or at geometric singularities (e.g., star concavities) where the one-sided support may be poorly conditioned. A brief discussion of this limitation or a sensitivity check would strengthen the paper."}],"tokens_in":22115,"tokens_out":748,"duration_ms":111272,"standing_objections":[]},"desk_editor":{"model":"glm-5.2","letter":"Short version: the paper identifies a real, previously unquantified systematic error in one-sided diffuse-interface IBMs — the effective boundary shifts inward because the spreading operator averages over interior points only — and proposes a lightweight correction that reduces Dirichlet errors by 77% and isothermal errors by 85% at negligible cost. The core analysis is sound and the validation is broad. It deserves a serious referee. Here is my take in more detail. What is genuinely new: the quantitative derivation of the inward boundary displacement (Eq. 25) and the target-value reconstruction at a virtual point located at this displaced position. The displacement analysis is clean — Eq. 25 is a direct consequence of the one-sided support, and Fig. 3 confirms it empirically. The reconstruction itself is straightforward linear interpolation along the normal, which is the right level of complexity for a correction that costs under 1.5% extra compute. The convergence study (Fig. 4) shows second-order accuracy is preserved, and the validation suite is solid: cylinders, stars, NACA0012, 3D sphere, rotating sphere, across subsonic to supersonic regimes, with good agreement to body-fitted and experimental references. The Neumann error increase of 8% is honestly reported and minor — for adiabatic walls the reconstruction reduces to M_V^t = M_P^*, which is the same as the original FODIBM, so no improvement is expected there. The stress-test concern about M_P^* being sampled from within the IBM forcing layer is worth raising with the authors, but I do not think it undermines the method. In steady state, once forcing converges, M_P^* reflects the physical near-wall gradient, and the validation cases support this. The concern is really about robustness in untested regimes — high-Re boundary layers, shock-boundary interactions, transient startup — not a fundamental flaw. The paper does not test these, and a referee should ask about sensitivity to strong wall-normal gradients. The linear interpolation assumption (Eqs. 26–27) is the other soft spot, but it is proportionate: for the grid resolutions and geometries tested, it works, and the star cases involve non-trivial curvature. No code or data is shipped, which prevents independent verification, but the method is specified clearly enough to reproduce. Self-citation is moderate and appropriate — the FODIBM framework comes from [33], but the new contribution here is independent of that. Who this is for: CFD practitioners working with diffuse-interface IBMs for compressible flows, particularly those who need accurate shock stand-off and near-wall predictions without body-fitted meshes. The paper is a useful, incremental methodological contribution. Recommend accepting for peer review.","headline":"Clean analysis of a systematic boundary shift in one-sided diffuse-interface IBMs, with a simple, cheap correction that works well across 2D and 3D compressible flows.","tokens_in":23082,"tokens_out":634,"would_cite":true,"duration_ms":82944,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["47.11.-j","47.40.-x","47.11.Df"],"model":"glm-5.2","headline":"Fixing a hidden boundary shift cuts immersed-boundary errors by 77-85%","keywords":["immersed boundary method","diffuse interface","compressible flow","lattice Boltzmann method","boundary condition enforcement","target-value reconstruction","one-sided spreading","shock stand-off distance"],"falsifier":"If one constructed a test case with strongly nonlinear near-wall profiles along the normal direction (e.g., a thin boundary layer on a sharply curved surface) and the linear interpolation between points B and P produced target values that degraded rather than improved boundary-condition accuracy, the core mechanism would be undermined. The paper's star geometries provide some curvature stress-testing, but the linear reconstruction has not been challenged under extreme near-wall gradient conditions.","tokens_in":22380,"feed_emoji":"📐","tokens_out":817,"duration_ms":105100,"temperature":0.7,"pith_summary":"This paper identifies a systematic geometric error in one-sided immersed boundary methods for compressible flow simulation. When the forcing term that enforces boundary conditions is spread only to the interior side of a boundary (a strategy that avoids unphysical pressure leaks), the effective location where the boundary condition is actually imposed shifts inward from the true geometric boundary. The authors quantify this displacement analytically and show it causes the simulated body to be effectively smaller than intended, degrading shock positions and surface quantities. They propose a target-value reconstruction: rather than directly imposing the desired boundary values, they compute corrected target values at the displaced effective-boundary location using linear interpolation between the geometric boundary and a nearby interior projection point, so that the intended condition is recovered at the true boundary after spreading. The correction is confined to the target-value evaluation step and leaves the interpolation and spreading operators unchanged, adding at most 1.4% computational overhead. The method handles both Dirichlet conditions (no-slip velocity, isothermal temperature) and Neumann conditions (adiabatic walls). Tested on cylinders, star geometries, airfoils, and spheres in subsonic through supersonic regimes, the corrected method reduces no-slip boundary errors by 77% and isothermal errors by 85% relative to the uncorrected version, while retaining second-order grid convergence and matching body-fitted reference solutions.","feed_headline":"Fixing a hidden boundary shift cuts immersed-boundary errors by 77-85%","feed_subtitle":"One-sided spreading in diffuse-interface methods silently moves the effective wall inward; a cheap linear correction restores it.","key_machinery":"The target-value reconstruction uses three points along the boundary normal: the geometric boundary point B where conditions are prescribed, the projection point P at a fixed normal distance inside the fluid where predicted flow values are interpolated, and the virtual point V located at the analytically computed effective boundary position. For Dirichlet conditions, linear interpolation between B and P yields the corrected target at V. For Neumann (zero-gradient) conditions, the target at V equals the value at P. These reconstructed targets replace the raw prescribed values in the forcing-term computation.","core_discovery":"The central discovery is that the asymmetric kernel support of one-sided spreading operators in diffuse-interface immersed boundary methods causes a quantifiable inward displacement of the effective boundary. This displacement is not a tunable artifact but a geometric consequence of averaging over interior Eulerian points only. The authors derive the displaced position from the spreading operator itself and show that compensating for it via linear target-value reconstruction at a virtual point restores boundary-condition accuracy to levels comparable with body-fitted methods, at negligible cost.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Asymmetric kernel shifts the effective wall inward in immersed boundary methods","Target-value reconstruction corrects boundary displacement in one-sided DIBM","One-sided spreading moves effective boundary inward; linear fix restores accuracy","Correcting inward boundary shift cuts immersed-boundary errors by up to 85%","Geometric boundary displacement in one-sided DIBM fixed with negligible cost"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The reconstruction assumes the flow field varies linearly along the normal direction between the geometric boundary point and the projection point. For geometries with high curvature or flows with steep gradients very close to the wall, this linear assumption could introduce errors, though the paper reports no significant issues in its star-geometry tests.","fun_headline_variants_meta":{"raw":{"variants":["Asymmetric kernel shifts the effective wall inward in immersed boundary methods","Target-value reconstruction corrects boundary displacement in one-sided DIBM","One-sided spreading moves effective boundary inward; linear fix restores accuracy","Correcting inward boundary shift cuts immersed-boundary errors by up to 85%","Geometric boundary displacement in one-sided DIBM fixed with negligible cost"]},"model":"glm-5.2","effort":"low","cost_usd":0.0,"raw_usage":{"total_tokens":662,"prompt_tokens":573,"completion_tokens":89,"prompt_tokens_details":null},"tokens_in":573,"tokens_out":89,"duration_ms":51306,"temperature":1.0,"reasoning_tokens":null,"cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-09T10:54:00.180803+00:00","model_set":{"reader":"glm-5.2"},"falsifier":"If one constructed a test case with strongly nonlinear near-wall profiles along the normal direction (e.g., a thin boundary layer on a sharply curved surface) and the linear interpolation between points B and P produced target values that degraded rather than improved boundary-condition accuracy, the core mechanism would be undermined. The paper's star geometries provide some curvature stress-testing, but the linear reconstruction has not been challenged under extreme near-wall gradient conditions.","supporting_citations":[],"review_version":1}