{"id":"bfa59807-bf57-477b-b965-03acea8d7b8f","arxiv_id":"2505.22920","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"A 3D monolithic Eulerian FSI solver using geometric VOF/PLIC interface capturing that keeps a sharp interface, conserves mass, and matches benchmark results on coarse grids, including a DNS of turbulent flow over a compliant wall.","lead":"This paper develops a three-dimensional fluid-structure interaction solver on a fixed Cartesian grid using a geometric volume-of-fluid (PLIC) method to keep the fluid-solid interface sharp. It shows the solver matches published benchmark results on much coarser grids than diffusive interface methods and applies it to turbulent channel flow over a deformable compliant wall.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The ad hoc reset of B to identity in near-interface cells (Sec. 2.2.2) is unexamined; if it alters hyperelastic stress where the solid is thin, the benchmark agreement and coarse-grid claim are not yet established.","rationale":"The paper’s central promise is that a sharp VOF/PLIC interface, unlike diffusive interface capturing, delivers accurate results on coarse grids. That promise requires the hyperelastic stress near the interface to be physically faithful, because it is exactly the near-interface region where the solid is thin and where deformation gradients are largest. The B=I reset is the one step in the algorithm that is explicitly ad hoc, is applied precisely in that region, and is not accompanied by any convergence or sensitivity study. The reader’s weakest_assumption correctly identifies this as load-bearing. My reading did not find a more serious internal inconsistency: the governing equations are standard, the fractional-step method is standard, and the benchmark suite is broad. The absence of released code or data makes the benchmark agreements harder to verify, but that is a reproducibility limitation rather than a demonstrated flaw. The proposed sensitivity check directly tests whether the reset is a benign clipping or a hidden stabilization, and therefore whether the coarse-grid claim can be accepted as stated. Since the reader already assigned CONDITIONAL, this concern reinforces that verdict without moving it.","tokens_in":22243,"tokens_out":4072,"duration_ms":45490,"concrete_test":"Rerun the soft-disk lid-driven cavity (§3.3) and the Saint Venant-Kirchhoff shear-flow reversibility test (§3.4) with ε_c ∈ {10^-12, 10^-10, 10^-8, 10^-6, 10^-4} and with the reset replaced by setting B=I only where φ=0 after clipping. Compare centroid trajectories, L1 shape error at final times, and the maximum |B| in cells with 0<φ<0.1. If these quantities vary materially with ε_c, the reset is a hidden stabilization and the coarse-grid accuracy claim needs qualification; if they are invariant, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that VOF/PLIC gives accurate FSI on coarse grids depends on the hyperelastic stress σ_ij^hy = G_s(B_ij − δ_ij) being correct at and near the interface, because this stress enters the one-continuum momentum equation through σ_ij = φ σ^s + (1 − φ) σ^f (Eq. 10). Section 2.2.2 states: 'To prevent the exponential growth of B near the interface due to the shearing motion in the fluid domain, we set B = I for φ_{i,j,k} < ε_c.' This resets all deformation history in every cell whose solid volume fraction falls below ε_c = 10^-8. The paper gives no analysis of how this reset interacts with the WENO-Z advection of B or with the traction balance at the interface. For a solid that is thin or highly stretched (the soft disk in §3.3 and the compliant-wall DNS in §3.6 both develop strongly stretched regions), a non-negligible fraction of the solid mass can pass through near-interface cells where B is being artificially restored to the identity, so the effective stiffness experienced by the solid is wrong. Because ε_c is also used to clip φ, cells with φ slightly above ε_c retain a tiny volume but can carry B values from previous deformation; the reset is therefore not a harmless clipping but a potentially load-bearing stabilization. The benchmark agreements could be sensitive to this stabilization, which would undermine rather than support the coarse-grid claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper develops a three-dimensional monolithic Eulerian framework for fluid-structure interaction (FSI) on a fixed Cartesian grid, using the geometric volume-of-fluid method with PLIC reconstruction and Lagrangian-Explicit split advection to capture the fluid-solid interface. The fluid and solid are treated in a one-continuum formulation with a volume-fraction-weighted momentum equation; hyperelastic solids are modeled with neo-Hookean or Saint Venant-Kirchhoff laws via the left Cauchy-Green deformation tensor B, whose advection is discretized with fifth-order WENO-Z. The solver is validated against a series of benchmarks: rigid slotted-disk advection, compliant wall and deformable disk in lid-driven cavities, a reversibility test for a disk in shear flow, a 3D deformable sphere in a lid-driven cavity, and DNS of turbulent channel flow with a compliant bottom wall. The authors claim that the VOF/PLIC approach maintains a sharp, stable interface without flotsam or spurious currents, and that its accuracy on coarse grids is comparable to diffusive interface-capturing methods on much finer grids.","tokens_in":22534,"tokens_out":3795,"duration_ms":39995,"significance":"If the central claims hold, this is a useful contribution: it extends geometric VOF/PLIC, with its mass-conservation and sharp-interface properties, to fully Eulerian FSI in three dimensions, including turbulent flows. The paper's strengths are its broad validation suite against independent published results (Zhao et al., Sugiyama et al., Ii et al., Valizadeh et al., Moser et al., Rosti and Brandt, Esteghamatian et al.), the grid-convergence and reversibility tests, and the absence of parameter fitting to reproduce benchmark targets. These features make the work potentially valuable for simulating compliant coatings, biofouling, and other soft-body flow interactions. However, the main technical risk is an ad hoc reset of the deformation tensor in near-interface cells, which is not analyzed, and the headline coarse-grid accuracy claim is supported only by qualitative comparisons in the key benchmark.","major_comments":[{"comment":"The reset 'B = I for phi_{i,j,k} < epsilon_c' is an ad hoc stabilization that discards all deformation history in cells whose solid volume fraction is below the clipping tolerance. Since the hyperelastic stress sigma^hy_ij = G_s(B_ij - delta_ij) enters the one-continuum momentum equation through Eq. (10), this reset can alter the effective stiffness experienced by thin or highly stretched solid regions, such as the soft disk in Sec. 3.3 and the compliant wall in Sec. 3.6. The manuscript provides no sensitivity study, no estimate of the solid mass affected, and no test of the reset's influence on the benchmark results. Please quantify the effect of epsilon_c (e.g., by varying it over several orders of magnitude for at least one benchmark) and, if possible, compare against a run without the reset. Without this analysis, the benchmark agreements and the coarse-grid accuracy claim are not fully established.","section":"Section 2.2.2"},{"comment":"The central claim that VOF/PLIC on a 128x128 grid agrees well with Sugiyama et al. on a 1024x1024 grid is supported primarily by qualitative shape overlays (Fig. 9) and a centroid trajectory plot (Fig. 11). The paper should provide quantitative error measures, such as the L2 error of the centroid trajectory or interface position relative to the reference fine-grid solution, and should also report the difference between the present 128x128 result and the reference 1024x1024 result. This is load-bearing for the paper's headline claim that sharp VOF/PLIC is as accurate on coarse grids as diffusive methods on much finer grids.","section":"Section 3.3 and Conclusions"},{"comment":"The turbulent channel flow with a compliant wall is presented as a demonstration of the framework's capability, but the comparison with past works (Esteghamatian et al., Rosti and Brandt, Wang et al.) is qualitative, and no grid-resolution study is reported for this case. The non-uniform wall-normal grid with a uniform near-interface region should be justified with a resolution study, and quantitative comparisons of at least the mean velocity profile, Reynolds stresses, and surface deformation statistics should be provided. As written, the turbulent FSI claim remains qualitative and is not yet supported at the same level as the lower-Reynolds-number benchmarks.","section":"Section 3.6"}],"minor_comments":[{"comment":"The clipping tolerance epsilon_c = 10^-8 is used 'for all problems' without justification; a brief explanation of how this value was chosen and whether results are sensitive to it would be helpful.","section":"Section 2.2.2"},{"comment":"The sign convention in the Adams-Bashforth update for B is confusing: the source term is added while the advection term is subtracted. Please clarify that this follows directly from Eq. (16) and define the notation for the advection term more explicitly.","section":"Section 2.2.1, Eq. (18)"},{"comment":"The legend includes 'Sugiyama et al. (128 x 128)' but the text does not discuss this comparison; please comment on how the present 128x128 result compares with Sugiyama's own 128x128 result, as this would directly support the coarse-grid claim.","section":"Fig. 11"},{"comment":"The manuscript contains production placeholders ('Received: Added at production', 'DOI: xxx/xxxx', 'Journal ;00:1-26') that should be removed before final submission.","section":"General"},{"comment":"No code or data are made available. For a numerical methods paper, releasing at least the benchmark setup and, ideally, the solver itself would greatly strengthen reproducibility and allow independent verification of the coarse-grid claim.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The novelty claim of being the first 3D VOF/PLIC FSI framework should be carefully checked against the recent literature; the cited Esmailzadeh and Passandideh-Fard work is 2D, but there may be other geometric-VOF FSI methods not cited here. The main technical risk is the B-reset in Section 2.2.2; if the sensitivity analysis requested in the major comments reveals a strong dependence on epsilon_c, the central claims would need substantial revision. The absence of code/data may be acceptable for the journal, but it makes the qualitative comparisons harder to assess."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This is a solid engineering paper that does something genuinely new: a fully Eulerian 3D FSI framework using geometric VOF/PLIC for hyperelastic solids in a one-continuum formulation. The novelty claim holds up—I am not aware of prior 3D work with this combination. The paper is also honest about its construction: it reuses established building blocks (Mahesh's kinetic-energy-conserving FVM, WENO-Z for B advection, PLIC+LE for the interface) and validates the combination carefully against external benchmarks. The grid-convergence study, the reversibility test in shear flow, and the compliant-wall DNS all check out as far as I can tell. The coarse-grid claim is the most interesting result: their 128x128 soft-disk trajectory matches Sugiyama et al.'s 1024x1024 WENO result. If that holds, it is a real practical advantage for turbulent simulations.\n\nThe soft spot the stress-test flags is real: the B=I reset for cells with phi < epsilon_c (Sec. 2.2.2). The paper justifies it as preventing exponential growth of B from fluid shearing, but it discards deformation history in exactly the cells where a thin solid's stress matters. The paper gives no sensitivity study with respect to epsilon_c, and no analysis of how the reset interacts with the stress jump at the interface. My read is that this is a numerical stabilization that could bias the effective stiffness for thin or highly stretched solids, but the benchmarks do not clearly expose it. This is worth a referee's attention, not a reason to reject.\n\nTwo minor issues: no code or data are released, which makes independent reproduction harder than it should be for a methods paper; and some benchmark comparisons are stated as 'excellent agreement' without quantified error bars (the L1/L2 plots help, but only for self-convergence). The turbulent DNS is compared qualitatively to Esteghamatian et al.; that is acceptable for a first demonstration, but not a strong quantitative check.\n\nOverall, this is serious, well-executed work. I would send it to peer review and ask for a sensitivity study of epsilon_c and the B=I reset, and inquire about code availability. If I were working on FSI, I would cite it.","headline":"Genuinely new 3D geometric-VOF FSI framework with extensive validation; the B=I reset near the interface is the main thing to probe, but this deserves peer review.","tokens_in":23172,"tokens_out":2202,"would_cite":true,"duration_ms":21397,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper develops a fixed-grid, one-continuum solver in which a sharp geometric volume-of-fluid interface (PLIC reconstruction, Lagrangian-Explicit advection) tracks a viscous hyperelastic solid through a deforming flow, and reports…","keywords":["fluid-structure interaction","geometric volume-of-fluid","PLIC interface reconstruction","viscous hyperelastic solids","left Cauchy-Green deformation tensor","turbulent channel flow","fixed Cartesian grid","one-continuum formulation"],"falsifier":"A concrete test is to run the shear-flow reversibility problem with a thin solid sheet whose thickness spans only one or two computational cells, and to vary the clipping tolerance between $10^{-6}$ and $10^{-10}$ while measuring the final shape error. If the sheet's deformation or the recovered shape changes with the tolerance, the $B=I$ reset is controlling the interface stress and the method's coarse-grid accuracy claim does not extend to thin solids.","tokens_in":22040,"feed_emoji":"🌊","tokens_out":11237,"duration_ms":104066,"temperature":0.7,"pith_summary":"This paper aims to show that the geometric volume-of-fluid (VOF) method, with piecewise-linear interface reconstruction (PLIC), can serve as the interface-capturing core of a three-dimensional monolithic solver for fluid-structure interaction. The solver treats the fluid and a viscous hyperelastic solid as a single continuum on a fixed Cartesian grid, tracking solid deformation through a deformation tensor field rather than through a moving mesh. The paper's central claim is that this sharp-interface approach avoids the classic VOF failure modes -- floating solid fragments and spurious surface currents -- and that a 128x128 run can match a diffusive interface-capturing method run on a 1024x1024 grid. If true, turbulent flows over deformable solids can be simulated on modest grids without problem-dependent stabilization or interface reinitialization.","feed_headline":"Sharp-interface FSI solver matches fine-grid results on coarse grids","feed_subtitle":"A geometric volume-of-fluid method keeps interfaces sharp and stable, so 128x128 runs rival 1024x1024 diffusive solvers.","key_machinery":"The central objects are the solid volume fraction $\\phi$, a cell-averaged Heaviside indicator, and the left Cauchy-Green deformation tensor $B$. The interface is captured geometrically: PLIC reconstructs a planar interface in each cell from $\\phi$ using finite-difference normal estimates and analytical volume relations, and Lagrangian Explicit directionally split advection moves the reconstructed segments, with cyclic sweep rotation and a clipping step that discards fragments below a tolerance of $\\epsilon_c = 10^{-8}$. Solid deformation is carried by $B$, transported by its upper-convected derivative using fifth-order WENO-Z (weighted essentially non-oscillatory) finite-difference advection, and then converted to hyperelastic stress through linear and nonlinear versions. The unified momentum and incompressibility equations are solved with a finite-volume fractional-step method, using a multigrid-preconditioned conjugate-gradient Poisson solve; near-interface cells with $\\phi < \\epsilon_c$ have their deformation tensor reset to the identity to prevent unbounded growth.","core_discovery":"The central claim is that a sharp geometric VOF/PLIC interface is not only viable but advantageous for three-dimensional FSI. According to the paper, the framework maintains a sharp fluid-solid interface and mass conservation by construction, produces no nonphysical solid fragments even when a soft body is stretched near a moving lid or pinched between surfaces, and remains free of spurious surface oscillations at steady states. The benchmark evidence includes a compliant wall in a lid-driven cavity, soft and stiff disks in a lid-driven cavity, a reversibility test for a nonlinear hyperelastic disk in shear flow, a sphere in a three-dimensional lid-driven cavity, and a DNS of turbulent channel flow over a deformable compliant wall. The authors report that the disk-centroid trajectory computed on a 128x128 grid agrees with the reference diffusive method on a 1024x1024 grid, and that the turbulent compliant-wall simulation reproduces previously reported spanwise-aligned deformation patterns, enhanced near-wall Reynolds stresses, and counter-rotating spanwise rolls inside the wall. They state that, to their knowledge, this is the first 3D FSI framework built on the geometric VOF/PLIC method and applied to turbulent FSI.","pith_inferences":["The apparent 64x resolution advantage is likely a property of sharp interface capturing rather than of VOF specifically; a similar gain should appear for any sharp-interface method paired with the same incompressible flow solver.","The $B=I$ reset ties accuracy to the clipping tolerance and to cell size relative to solid thickness; thin or highly stretched solids are the regime where the method's interface-stress treatment would need a more principled way to keep deformation history.","Because solid shapes are initialized by prescribing $\\phi$, the framework is naturally suited to complex surface geometries; a testable extension is simulating a turbulent boundary layer over a patch of compliant roughness similar to biofouling.","The observed spanwise roll structure inside the compliant wall suggests the method could be used to systematically scan wall parameters such as stiffness, thickness, and viscosity for drag reduction, a direction the paper does not pursue."],"forward_implications":["Coarse-grid parity: a VOF/PLIC interface on 128x128 matches a diffusive WENO interface on 1024x1024 for the disk centroid trajectory, so users can exchange grid resolution for interface sharpness.","No fragments or oscillations: the solver reports no flotsam under severe stretching and pinching, and no spurious surface oscillations at equilibrium, so long-time FSI runs retain mass and stability.","No problem-dependent stabilization: unlike level-set or diffusive methods, the framework does not require reinitialization or fine grids to keep the interface sharp.","Turbulent applicability: the DNS of a compliant wall reproduces spanwise-aligned deformation patterns, enhanced Reynolds stresses, and counter-rotating spanwise rolls that resemble surface waves, demonstrating the solver can handle turbulent FSI.","Non-uniform meshes: aspect-ratio tests show the implementation works for cuboidal cells with AR=1, 2, and 4, which is needed for practical boundary-layer meshes."],"supporting_citations":[{"why":"Supplies the diffusive full-Eulerian FSI baseline that the VOF/PLIC results are compared against, including the 1024x1024 reference trajectory.","marker":"52"},{"why":"Provides fixed-mesh reference solutions for the compliant-wall and stiff-disk lid-driven cavity benchmarks.","marker":"45"},{"why":"Provides the full-Eulerian FSI method and the Saint Venant-Kirchhoff shear-flow reversibility setup used as a nonlinear benchmark.","marker":"13"},{"why":"Establishes the geometric VOF/Lagrangian-Explicit advection approach that the interface transport step is built on.","marker":"60"},{"why":"Documents the directionally split LE advection procedure and the clipping step used to suppress round-off fragments.","marker":"70"},{"why":"Supplies the fifth-order WENO reconstruction used for the deformation-tensor advection and for the diffusive reference method.","marker":"3"},{"why":"Supplies the WENO-Z weights that reduce dissipation in the deformation-tensor advection.","marker":"2"},{"why":"Provides the level-set Eulerian DNS of channel flow over a compliant wall that the turbulent results are compared with.","marker":"5"},{"why":"Provides the VOF/WENO turbulent compliant-wall DNS that motivated the material parameters and the stress-balance analysis.","marker":"6"},{"why":"Provides the 3D phase-field Eulerian FSI benchmark used to validate the sphere in a lid-driven cavity.","marker":"86"}],"fun_headline_variants":["VOF/PLIC FSI: sharp interfaces at coarse-grid cost","Sharp VOF keeps FSI stable, matches fine-grid accuracy","First 3D sharp-interface FSI solver, tested in turbulence","Geometric VOF gives sharp FSI without fine-grid toll","Coarse grids, sharp interfaces: VOF-based FSI proves out"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is the ad hoc rule that cells holding less than a tiny volume fraction of solid have their deformation history erased (the tensor $B$ is reset to the identity), which must not distort the hyperelastic stress that drives the interface.","fun_headline_variants_meta":{"raw":{"variants":["VOF/PLIC FSI: sharp interfaces at coarse-grid cost","Sharp VOF keeps FSI stable, matches fine-grid accuracy","First 3D sharp-interface FSI solver, tested in turbulence","Geometric VOF gives sharp FSI without fine-grid toll","Coarse grids, sharp interfaces: VOF-based FSI proves out"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000265,"raw_usage":{"total_tokens":1704,"prompt_tokens":1136,"completion_tokens":568,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":752,"completion_tokens_details":{"reasoning_tokens":476}},"tokens_in":752,"tokens_out":568,"duration_ms":5775,"temperature":1.0,"reasoning_tokens":476,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T12:56:57.866318+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A concrete test is to run the shear-flow reversibility problem with a thin solid sheet whose thickness spans only one or two computational cells, and to vary the clipping tolerance between $10^{-6}$ and $10^{-10}$ while measuring the final shape error. If the sheet's deformation or the recovered shape changes with the tolerance, the $B=I$ reset is controlling the interface stress and the method's coarse-grid accuracy claim does not extend to thin solids.","supporting_citations":[{"cited_title":"A full Eulerian finite difference approach for solving fluid–structure coupling problems","cited_arxiv_id":null,"evidence_quote":"Supplies the diffusive full-Eulerian FSI baseline that the VOF/PLIC results are compared against, including the 1024x1024 reference trajectory."},{"cited_title":"A fixed-mesh method for incompressible flow–structure systems with finite solid deformations","cited_arxiv_id":null,"evidence_quote":"Provides fixed-mesh reference solutions for the compliant-wall and stiff-disk lid-driven cavity benchmarks."},{"cited_title":"An implicit full Eulerian method for the fluid–structure interaction problem.International Journal for Numerical Methods in Fluids","cited_arxiv_id":null,"evidence_quote":"Provides the full-Eulerian FSI method and the Saint Venant-Kirchhoff shear-flow reversibility setup used as a nonlinear benchmark."},{"cited_title":"V olume-of-fluid interface tracking with smoothed surface stress methods for three-dimensional flows","cited_arxiv_id":null,"evidence_quote":"Establishes the geometric VOF/Lagrangian-Explicit advection approach that the interface transport step is built on."},{"cited_title":"Numerical prediction of drag reduction and interfacial shapes over superhydrophobic surfaces","cited_arxiv_id":null,"evidence_quote":"Documents the directionally split LE advection procedure and the clipping step used to suppress round-off fragments."},{"cited_title":"A monolithic finite element method for phase-field modeling of fully Eulerian fluid–structure interaction","cited_arxiv_id":null,"evidence_quote":"Provides the 3D phase-field Eulerian FSI benchmark used to validate the sphere in a lid-driven cavity."}],"review_version":1}