{"id":"f39eb652-65cb-4491-8b3d-d9a6310ce842","arxiv_id":"2607.05137","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":6.5,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"SoPlasmaFoam delivers an OpenFOAM multi-region plasma-dielectric solver plus evidence that ROUNDF beats standard TVD/SG schemes for streamers, that outer Poisson-transport correctors remain essential even under semi-implicit Poisson and low Courant numbers, and that a matrix-coefficient wall BC stay","lead":"SoPlasmaFoam is a new open-source OpenFOAM plasma solver that handles streamers and dielectric-barrier discharges with adaptive mesh refinement and multi-region coupling. Its tests show which numerical schemes and coupling loops actually control accuracy, giving practical guidance for plasma codes used in combustion, processing, and flow control.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified","rationale":"The manuscript’s strongest claims are comparative numerical findings obtained under a fixed physical model (LFA, analytical or BOLSIG+ tables, no photoionization). Because every scheme and every corrector count is evaluated on the same equations and the same Bagheri benchmark, absolute model error cancels in the ranking. The reader correctly flags LFA/photoionization as the principal physical caveat, yet that caveat does not undermine the reported scheme superiority, the necessity of outer loops, or the matrix-coefficient BC derivation (Eqs. 29–33). Performance and multi-region demonstrations are secondary and adequately supported. Consequently the ACCEPT verdict stands; the only useful remaining check is a controlled photoionization sensitivity that would confirm (or bound) transferability of the numerical conclusions.","tokens_in":35080,"tokens_out":455,"duration_ms":4149,"concrete_test":"Re-run the Case-A streamer series of Figures 10–13 with the identical ROUNDF / SG / MUSCL settings but with a simple photoionization source (e.g. Zheleznyak three-group) added; if the relative ordering of schemes or the number of outer correctors required for |E|max convergence changes by more than one corrector or reverses the ROUNDF–SG ranking, the transferability claim would need qualification.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The three central numerical claims (ROUNDF ranking, necessity of outer Poisson-transport correctors even under semi-implicit Poisson and Co/Cε ≪ 1, and the matrix-coefficient wall BC) rest on controlled comparative experiments against the Bagheri et al. streamer benchmark and a stiff advection problem, not on the absolute fidelity of LFA. The reader’s weakest assumption (LFA + omitted photoionization) is real for quantitative surface-charge or absolute field values in Sections 6–7, but it is not load-bearing for the scheme-ranking or coupling conclusions: those conclusions are relative and survive under the same physical model used by the reference codes. No internal inconsistency, circularity, or untested numerical claim that would overturn the ACCEPT verdict was found.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"SoPlasmaFoam is an open-source OpenFOAM multi-region drift-diffusion–Poisson solver for streamers and dielectric-barrier discharges, with PETSc (CPU/GPU), blastAMR (hex/polyhedral, 1D–3D/axisymmetric), ROUND convective schemes, and monolithic plasma–dielectric Poisson coupling. The paper’s three methodological claims are: (i) on a stiff 1D advection problem and the Bagheri et al. positive-streamer benchmark, Scharfetter–Gummel is stable but overly diffusive on coarse meshes while ROUNDF outperforms standard TVD limiters; (ii) outer fixed-point (PIMPLE) Poisson–transport correctors critically control accuracy even when Courant and dielectric-relaxation numbers are well below unity, and a semi-implicit Poisson formulation does not remove that need; (iii) a wall boundary condition that writes thermal/drift fluxes into matrix coefficients remains well-posed in the drift-dominated (high cell-Péclet) limit where the conventional mixed-boundary mapping fails. Validation covers a low-pressure DC glow (Derzsi et al.), the positive-streamer benchmark (Cases A/B), a nanosecond SDBD multi-region demonstration, and single-node strong scaling with and without AMR.","tokens_in":35196,"tokens_out":1326,"duration_ms":18310,"significance":"If the scheme ranking, coupling analysis, and wall-BC formulation hold, the paper supplies transferable numerical guidance for the plasma-fluid community, not only another OpenFOAM solver. The controlled corrector-loop study (explicit and semi-implicit, several Δt and mesh sizes) is particularly useful: it quantifies a practice that is often left as folklore. Open release with modular run-time selection, monolithic multi-region Poisson, and blastAMR on non-Cartesian meshes is a concrete infrastructure contribution for streamer/DBD and multiphysics work (flow control, PAC). Performance with AMR is competitive with the fastest codes reported on the same benchmark. Strengths include external multi-code validation (Bagheri et al., Derzsi et al.), systematic scheme and corrector experiments, and an explicit derivation of the mixed-BC failure mode.","major_comments":[{"comment":"§3.3 (Eqs. 20–33) and Abstract contribution (iii): the mixed-boundary failure in the drift-dominated limit is derived carefully, and the matrix-coefficient wall BC is well motivated. However, none of the validation cases (§5–7) isolates this BC with a controlled comparison (mixed vs matrix-coefficient) under high cell Péclet number. The DC-glow BCs differ from the thermal-drift wall model; the freestream streamer does not exercise walls; the SDBD uses dielectric surface charging without a side-by-side BC test. Because this is listed as one of three main contributions and the abstract asserts that the BC “remains accurate” where mixed mappings fail, a short 1D or quasi-1D drift-dominated wall test (or a wall-bounded streamer/sheath comparison) is needed to substantiate the claim, not only the algebraic argument.","section":null},{"comment":"§6.3.1 / Figs. 11–13: the conclusion that outer correctors remain necessary under semi-implicit Poisson and for Co and Cε well below unity is central and well supported for Case A with ROUNDF. The manuscript should state more explicitly the recommended practical rule (e.g., minimum correctors vs max Co and Cε) and whether the same corrector counts apply under Scharfetter–Gummel or on Case B, where gradients are steeper. Without that, readers may over-generalize the 1–4 corrector findings from a single scheme and background density.","section":null}],"minor_comments":[{"comment":"Section 4 title: “Assessement” → “Assessment”.","section":null},{"comment":"§3.4: typo “assembilng” → “assembling”.","section":null},{"comment":"Eq. (40): analytical solution n(x,t)=n0(x e^{At}) e^{At} is hard to parse in the text rendering; clarify the composition (argument of n0 vs multiplicative factor).","section":null},{"comment":"Table 2 / §6.3.3: performance comparisons mix different processors, core counts, Δt policies, and corrector counts. A short caveat paragraph (already partly present) should state that wall times are indicative, not a strict ranking.","section":null},{"comment":"§7: SDBD surface-charge comparison (SG vs ROUNDF, Fig. 23) is interesting; note briefly whether the same outer-corrector and time-step criteria were used for both schemes so the order-of-magnitude charge difference is not confounded by coupling settings.","section":null},{"comment":"Naming: SoPLASMA suite vs SoPlasmaFoam solver is clear in the introduction but could be stated once in the abstract for discoverability.","section":null},{"comment":"Photoionization and LMEA are correctly scoped out; a one-sentence forward pointer in §6 that Case B (low background) is the regime where photoionization usually matters most would help non-specialist readers interpret residual mesh sensitivity.","section":null},{"comment":"Figure 1 TVD diagram: ensure the blue second-order region and Superbee/ROUNDF loci remain legible in grayscale print.","section":null}],"recommendation":"minor_revision","confidential_remarks":"I agree with the reader’s ACCEPT-leaning assessment on the scheme and coupling claims; those rest on external benchmarks and controlled numerics and are not circular. My minor_revision is driven mainly by the under-demonstrated wall BC, which the abstract elevates to a primary contribution. A short dedicated test would resolve this without expanding scope. Fit for a computational plasma / CPC-style methods venue is good; novelty relative to SOMAFOAM, reactPlasFOAM, and Vidyut3d is adequately differentiated in §1.3."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"This is a usable OpenFOAM-based multi-region plasma-dielectric solver (PETSc, blastAMR polyhedral AMR, ROUND schemes, monolithic interface Poisson) plus three concrete numerical findings that matter for anyone writing fluid streamer codes: ROUNDF beats the usual TVD set and Scharfetter-Gummel on the Bagheri streamer benchmark, outer fixed-point correctors still control accuracy even under semi-implicit Poisson and Co/Cε well below 1, and a matrix-coefficient wall BC that stays correct in the drift-dominated limit where the mixed mapping fails.\n\nWhat is new is the combination and the controlled experiments, not a new physical model. Relative to SOMAFOAM, Vidyut3d, reactPlasFOAM and Afivo the architecture is distinct (unstructured/polyhedral AMR + monolithic multi-region + ROUND + PETSc). The scheme ranking, corrector-loop study and wall BC are clean comparative tests on the stiff advection problem and the external Bagheri multi-code streamer case; they are not circular. Validation against Derzsi glow and Bagheri is thorough; AMR performance numbers put it among the faster reported codes on that benchmark. The SDBD demo shows the multi-region path works and produces densities/fields of the expected order.\n\nSoft spots are real but secondary. Everything is LFA with photoionization left out; that limits absolute surface-charge and field values in the SDBD, but the scheme and coupling claims are relative and survive under the same physics the reference codes used. One glow comparison used manually digitized plots. No public repo/commit is given in the text, which hurts immediate reproducibility. Scaling is the expected memory-bound FVM story; single-node only. None of this overturns the central numerical results.\n\nThis is for people who build or use fluid plasma codes for streamers, DBDs, actuators or plasma-assisted combustion. It deserves a serious referee. I would cite the scheme ranking and the corrector-loop result, and I would engage with the code once it is released. Send it to review.","headline":"Solid open multi-region AMR plasma solver with three transferable numerical results that hold up under the same LFA model used by the community benchmarks.","tokens_in":35842,"tokens_out":513,"would_cite":true,"duration_ms":5599,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"For accurate streamer simulations, the flux scheme and outer Poisson-transport correctors matter more than Courant or dielectric-relaxation limits alone, and a matrix-level wall condition fixes the drift-dominated failure of mixed boundary","keywords":["streamer","low-temperature plasmas","dielectric barrier discharge","adaptive mesh refinement","flux schemes","Poisson-transport coupling","OpenFOAM","drift-diffusion"],"falsifier":"Re-run the Bagheri positive-streamer Case A and Case B with the same meshes and time steps but a local-mean-energy model plus photoionization; if maximum field and reduced streamer length then diverge systematically from the ROUNDF multi-corrector results, the local-field plus pure-transport claim is false for those regimes.","tokens_in":35943,"feed_emoji":"⚡","tokens_out":1109,"duration_ms":12355,"temperature":0.7,"pith_summary":"This paper introduces SoPlasmaFoam, an open-source multi-region plasma-dielectric solver on OpenFOAM, and uses it to settle three practical questions that control streamer and surface-discharge accuracy. First, among common convective schemes, Scharfetter-Gummel is stable but overly diffusive on coarse meshes, while the ROUNDF limiter beats every tested TVD scheme on a stiff advection problem and on the positive-streamer benchmark. Second, the number of fixed-point correction loops that re-couple Poisson and species transport each time step is a first-order accuracy control: a semi-implicit Poisson form does not remove the need for those loops, and even Courant and dielectric-relaxation numbers well below one still require tightening. Third, a wall boundary condition written directly into the discretized matrix coefficients stays accurate when drift dominates, where the usual mixed-boundary mapping drives the face density to zero or produces unphysical overshoots. Validated on a DC glow, free positive streamers, and a nanosecond surface DBD, and competitive in wall time once adaptive mesh refinement is on, the work gives concrete numerical rules other plasma-fluid codes can adopt.","feed_headline":"ROUNDF and tight coupling fix streamer accuracy","feed_subtitle":"Even sub-unity Courant numbers need outer Poisson correctors; a matrix wall BC stops drift-limit failure","key_machinery":"Drift-robust wall boundary condition on matrix coefficients: instead of prescribing a face value fraction in a mixed BC, the outward drift and thermal fluxes are inserted as implicit contributions to the boundary-cell diagonal, so the correct wall flux is recovered even when diffusion is negligible relative to drift.","core_discovery":"The central claim is that three methodological choices dominate streamer and dielectric-barrier accuracy: use ROUNDF for the drift flux rather than Scharfetter-Gummel or standard TVD limiters; keep outer fixed-point Poisson-transport correctors even under semi-implicit Poisson and sub-unity Courant/dielectric-relaxation numbers; and enforce wall fluxes by writing thermal-plus-outward-drift terms into the matrix coefficients instead of mapping them onto a mixed boundary condition that fails at high cell Péclet number.","pith_inferences":["The same matrix-coefficient wall treatment should transfer to other finite-volume plasma codes that still use mixed BCs and would otherwise under-predict ion collection at high Péclet number.","If photoionization and an electron energy equation are added, the paper’s corrector-loop study should be repeated: non-local ionization may change how many outer iterations are needed per time step.","The finding that semi-implicit Poisson does not remove outer loops suggests similar fixed-point requirements will appear in multiphysics couplings (plasma-flow, plasma-chemistry) built on the same modular stack.","Memory-bound single-node scaling implies that GPU PETSc backends and load-balanced AMR will matter more than raw core count for 3-D streamer trees and surface DBDs."],"forward_implications":["Streamer codes should default to ROUNDF (or an equivalent high-resolution ROUND limiter) rather than Scharfetter-Gummel on anything coarser than a few micrometres.","Stability criteria based only on Courant and dielectric-relaxation numbers are insufficient; outer Poisson-transport corrector counts must be reported and converged separately.","Semi-implicit Poisson formulations still require those outer loops; they buy larger time steps but do not replace tight coupling.","Wall BCs for ions and electrons in the drift-dominated sheath should be implemented at matrix-coefficient level, not as mixed face-value maps.","With adaptive mesh refinement the same OpenFOAM-based framework reaches wall-clock times competitive with the fastest published streamer codes on the standard benchmark."],"fun_headline_variants":["ROUNDF tops TVD and Scharfetter-Gummel for streamer flux","Outer Poisson correctors required even at sub-unity Courant","Matrix wall BC stops high-Péclet drift boundary failure","ROUNDF plus tight Poisson loops dominate streamer accuracy","Drift-robust matrix BC enables multi-region DBD fidelity"],"cache_read_input_tokens":32896,"weakest_assumption_plain":"Transport and ionization rates depend only on the local reduced electric field (local-field approximation), with no electron energy equation and no photoionization, so the reported agreement holds only while that local-equilibrium picture remains valid.","fun_headline_variants_meta":{"raw":{"variants":["ROUNDF tops TVD and Scharfetter-Gummel for streamer flux","Outer Poisson correctors required even at sub-unity Courant","Matrix wall BC stops high-Péclet drift boundary failure","ROUNDF plus tight Poisson loops dominate streamer accuracy","Drift-robust matrix BC enables multi-region DBD fidelity"]},"model":"grok-4.5","effort":"low","cost_usd":0.005402,"raw_usage":{"total_tokens":1549,"prompt_tokens":925,"num_sources_used":0,"completion_tokens":75,"cost_in_usd_ticks":54020000,"prompt_tokens_details":{"text_tokens":925,"audio_tokens":0,"image_tokens":0,"cached_tokens":128},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":549,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":925,"tokens_out":75,"duration_ms":5410,"temperature":1.0,"reasoning_tokens":549,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-11T08:13:15.500400+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Re-run the Bagheri positive-streamer Case A and Case B with the same meshes and time steps but a local-mean-energy model plus photoionization; if maximum field and reduced streamer length then diverge systematically from the ROUNDF multi-corrector results, the local-field plus pure-transport claim is false for those regimes.","supporting_citations":[],"review_version":1}