{"id":"11baa9e4-bd32-456a-b915-394b07fad088","arxiv_id":"2411.16369","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A high-order discontinuous-Galerkin discrete-ordinates neutron transport code is derived, implemented, and validated against analytical, literature, and Monte Carlo benchmarks in 1D and 3D fusion blanket geometry.","lead":"A new deterministic neutron transport solver combines discontinuous Galerkin spatial discretization with discrete ordinates and multigroup energy groups to model fusion blanket neutronics much faster than Monte Carlo. Benchmarks against analytical solutions and OpenMC show convergence and agreement within a few percent for most energies, supporting its use in early-stage reactor design.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The advertised fast 3D fusion-reactor capability is not yet supported: the only 3D test is a rectangular cutout in a slab, no speed comparison is reported, and the authors explicitly defer both to future work.","rationale":"The reader's weakest-assumption choice, the neglect of group-to-group upscatter, is a real physical limitation and is correctly identified in Section 2.1 and Section 4.3. However, it is acknowledged, explicitly isolated to E < 10 eV, and does not affect the headline tritium-breeding result (1.5% agreement), so I do not regard it as the single most load-bearing issue. The more consequential gap is that the method's stated purpose—fast, accurate 3D neutronics for fusion design—is tested only on slab-like geometry with rectangular cutouts, and the speed advantage is asserted without numbers. The paper's own conclusion concedes that a more complex 3D reactor geometry and speed comparisons are future work. This does not invalidate the derivations, which appear internally consistent, or the convergence tests, which support the implementation for the tested geometries. It does mean the central claim as advertised is not yet established. The appropriate verdict is therefore CONDITIONAL, matching the reader's verdict, so no verdict change is needed. A missing code/data release is a further reproducibility concern, but it is secondary to the missing scope-of-validation evidence.","tokens_in":22573,"tokens_out":8027,"duration_ms":84124,"concrete_test":"Run the Section 4.4 blanket benchmark on a toroidal-sector or stellarator-like unstructured tetrahedral mesh with curved surfaces, using the same nuclear data treatment, and compare scalar flux and TBR against a converged continuous-energy OpenMC run on the identical geometry; record wall-clock time, CPU-hours, and memory for both codes at matched accuracy. If the deterministic code does not reproduce TBR to roughly 1.5% and local scalar flux to roughly 10% (the accuracies claimed for the slab cases), or if its CPU time is not substantially lower than OpenMC's, the abstract's 'quickly and accurately ... three-dimensional geometry' claim is not supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The abstract promises a method 'capable of quickly and accurately assessing the neutron response of a fusion reactor, even in three-dimensional geometry.' For this central claim to hold, two things must be true: the unstructured DG sweep and matrix-free solvers must remain accurate and robust on genuinely reactor-like 3D meshes, and the method must actually be faster than Monte Carlo in a fair comparison. Neither is demonstrated. Section 4.4 is the only 3D inhomogeneous benchmark, and it uses a slab with rectangular, axis-aligned void cutouts and cross sections generated from the 1D problem; it does not exercise curved boundaries, toroidal/helical geometry, or the unstructured-mesh flexibility that motivates the method. No wall-clock or CPU-hour table is provided; the speed claim rests on the statement that the deterministic code 'use significantly less time CPU-hours in all considered cases.' The conclusion explicitly states that 'before using it in reactor design or optimization, it should be benchmarked with established codes in a more complex, three-dimensional reactor geometry, including computational speed comparisons. This is the subject of a future paper.' Thus the central claim as advertised is ahead of the evidence. This is not an internal inconsistency, but it is load-bearing: if a curved-geometry benchmark or a fair timing comparison fails, the paper's value proposition for fusion design collapses.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript presents a deterministic neutron transport solver aimed at early-stage fusion design. The method combines multigroup energy discretization (solved from high to low energy under the no-group-to-group-upscatter assumption), discrete-ordinates angular discretization with TN quadratures, arbitrary-order discontinuous Galerkin spatial discretization on straight-edged convex elements, Legendre-expanded anisotropic scattering, and matrix-free GMRES/BiCGSTAB inner iterations on spherical-harmonic flux moments; the upwind DG flux yields a per-element transport sweep whose matrix assembly and inversion are element-local (Eq. 22), with a quadrature-free simplification for simplexes (Appendix C). Verification proceeds in three stages: an analytical slab problem showing optimal error scaling N^-(p+1) in space for p = 0-4 and Q^-1 in angle; the Reed isotropic-scattering test and a two-group anisotropic-scattering test, which agree with the multigroup mode of OpenMC to within about 2% in well-resolved regions; and a helium-cooled-pebble-bed blanket benchmark against continuous-energy OpenMC using FENDL/TRANSX and OpenMC-generated multigroup cross sections, agreeing within 10% for E > 10 eV and within 1.5% on tritium breeding, with larger deviations below 10 eV traced to the upscatter assumption. A single three-dimensional benchmark with rectangular void cutouts in the blanket slab is also reported, using the OpenMC-generated cross sections.","tokens_in":22789,"tokens_out":24368,"duration_ms":196872,"significance":"If the results hold, this is a genuinely useful tool for the fusion design toolbox: a deterministic solver with demonstrated high-order spatial convergence, a memory-efficient moment-only formulation (Eq. 33), honest and quantified treatment of the upscatter approximation (Fig. 13), and validation against independent references (analytical solution; OpenMC in both multigroup and continuous-energy modes) with cross sections taken from FENDL and from OpenMC rather than fitted to benchmark outputs; there are no free parameters in the derivations. The paper's strengths include explicit assumption statements (Section 2.1), the element-independent calligraphic-matrix construction that makes high-order simplex sweeps quadrature-free (Appendix C), and the clean separation of verification (Section 3) from application (Section 4).","major_comments":[{"comment":"The abstract claims a method 'capable of quickly and accurately assessing the neutron response of a fusion reactor, even in three-dimensional geometry,' but the reported evidence supports only part of this claim. No wall-clock, CPU-hour, or iteration-count figures appear anywhere in the manuscript; the only quantitative efficiency statement is the qualitative remark in §4.4 that the deterministic code 'use[s] significantly less time CPU-hours in all considered cases,' and the conclusions (§5) explicitly defer benchmarking 'in a more complex, three-dimensional reactor geometry, including computational speed comparisons' to a future paper. Moreover, the only fully three-dimensional inhomogeneous benchmark (§4.4) is a slab with two axis-aligned rectangular void beams, using cross sections generated from the one-dimensional problem, so it does not exercise curved or toroidal geometry, and the mesh is effectively Cartesian rather than genuinely unstructured. Section 2.8 further notes that only angle-parallelization has been used and that scaling is future work. The fix is within scope: either temper the abstract and §1 to claim demonstrated accuracy on slab-like geometries with speed presented as a qualitative observation, or add a minimal quantitative performance comparison (e.g., a CPU-time or iteration-count table for the Section 4 blanket case). As written, the headline claim is ahead of the evidence.","section":"Abstract; §4.4; §5"},{"comment":"The abstract's 'accurately assessing' claim is unqualified, but the method deliberately neglects group-to-group upscatter (§2.1), and the authors' own measurements show the consequences: Fig. 13 demonstrates that the upscatter assumption 'partly explains the observed differences' for E < 10 eV, where Figs. 11 and 16 show deterministic/OpenMC disagreements at the blanket edge that exceed the 10% figure quoted for E > 10 eV. The paper is admirably transparent about this limitation in the body text, so the issue is claim scope rather than a hidden flaw: the abstract should state the demonstrated domain of validity, namely energies above roughly 10 eV and integral quantities such as tritium breeding (within 1.5% of OpenMC) in the tested slab-like geometries. Without this qualification, the abstract overstates the method's accuracy in the thermal range.","section":"§2.1; §4.3; Fig. 13"},{"comment":"The three-dimensional benchmark uses only the OpenMC-generated multigroup cross sections from the one-dimensional configuration ('Only OpenMC-generated cross sections (from the 1D problem) are used'), and no three-dimensional run with the FENDL/TRANSX cross sections is reported. This is not circular in the strict sense, because the reference solution is continuous-energy OpenMC and the cross sections are inputs rather than fits, but it does reduce the independence of the 3D validation: the multigroup data embedded in the deterministic solve were produced by the same code against which the solution is compared, on the parent configuration of the modified 3D case, while the FENDL path that a design tool would actually use is validated only in 1D. Either a single FENDL-based 3D run (even with the expected lower agreement in the breeding zone) or an explicit statement that §4.4 is a cross-section-transferability demonstration rather than a validation of the FENDL chain would make the scope of the 3D claim precise.","section":"§4.4"}],"minor_comments":[{"comment":"The abstract as circulated contains the duplicated phrase 'capable of quickly and quickly assessing,' whereas the abstract inside the manuscript reads 'capable of quickly and accurately assessing'; the duplication should be removed and the two versions made identical.","section":"Abstract"},{"comment":"Several typos should be corrected: 'benificial' (§1), 'this is comes' (§2.1), 'quadarature' (§3.2), and 'the mimum feature size' (Fig. 7 caption).","section":"Throughout"},{"comment":"The convergence-order notation is inconsistent: §3.1 states 'optimal N^{p+1} convergence rate' and §3.3/Fig. 10 state 'N^{-p+1},' while the plotted fits in Figs. 4 and 10 are N^-1, N^-2, N^-3, N^-4, N^-5 for p = 0-4, i.e., error proportional to N^-(p+1); the text and captions should be unified on this form.","section":"§3.1; §3.3; Fig. 10"},{"comment":"The Legendre expansion of the scattering cross section is written in Eq. (6) without the (2l+1) factor but in Eq. (A.3) with it; the footnote in Appendix A explains the convention, but a forward pointer in §2.3 would prevent readers from misassembling Eq. (7).","section":"§2.3, Eq. (6); Appendix A, Eq. (A.3)"},{"comment":"The statement that topologically sorting the inflow-dependency graph 'yields a solution order' should be qualified: cyclic sweep dependencies are a known phenomenon for arbitrary unstructured S_N meshes (see Ref. [10]), so the authors should state the conditions under which the graph is guaranteed to be acyclic or describe the fallback (e.g., iteration) used when it is not.","section":"§2.4"},{"comment":"The sentence 'use significantly less time CPU-hours in all considered cases' should specify the conditions of the comparison (serial versus parallel settings, machine, numbers of cores, and whether the OpenMC tallies were converged) so that the reader can at least reproduce the setup of the qualitative speed statement.","section":"§4.4"},{"comment":"No convergence check is reported in the three-dimensional geometry (the TN9 quadrature set is chosen 'to limit ray-effects' and the mesh is refined once); a single refinement or quadrature-order test in 3D would show that the residual differences in Fig. 16 are not discretization-driven.","section":"§4.4"},{"comment":"The paper states that one-, two-, and three-dimensional models are implemented, but no two-dimensional benchmark is presented; a sentence clarifying whether the 2D models are exercised only as special cases of the 3D runs would close this gap.","section":"§2.8"},{"comment":"The vertical axis of Fig. 6 is labeled phi [m^-3], whereas comparable flux plots elsewhere (e.g., Fig. 9) use phi [m^-2 s^-1]; the units should be harmonized and checked.","section":"Figs. 6 and 9"},{"comment":"The operator M that converts angle values to moment values shares its symbol with the element M of §2.4 and with the moment space M defined in the same paragraph; renaming the operator (for example, Phi) would remove a genuine source of confusion.","section":"§2.6"},{"comment":"References [19] (Lyytinen et al., Nuclear Fusion, 2024) and [21] (Boyd et al., Nuclear Technology, 2019) lack complete volume/page or article identifiers.","section":"References"},{"comment":"The manuscript does not state whether the code or the benchmark input files will be made available; a data/code availability statement would materially aid reproducibility of the verification results.","section":"Code availability"}],"recommendation":"major_revision","confidential_remarks":"For the editor: the technical core of this manuscript is sound and the verification program is well designed, so the decision hinges on scope rather than correctness. I am recommending major revision primarily because the abstract and introduction present as demonstrated a capability that the paper itself concedes is future work (fast, reactor-like 3D benchmarking). If the authors add a minimal performance comparison or reword the claims to match the demonstrated evidence, the paper would be publishable in my view. One novelty-scope note: DG-based S_N sweeps are not new in themselves (Refs. [9, 10] are close relatives); the genuinely new elements appear to be the unified 1D/2D/3D simplex implementation with element-independent matrices and the matrix-free moment-only inner iteration, and the paper would benefit from a sharper differentiation on exactly those points. No citation-pattern concerns beyond the incomplete references noted in the minor comments."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Worth a serious referee. The paper is a methods paper, not a demonstration of the headline capability. What's actually new: a specific combination of arbitrary-order DG, discrete ordinates, multigroup energy, anisotropic scattering, matrix-free GMRES/BiCGSTAB, and a unified 1D/2D/3D simplex formulation with reference-element matrices. The derivation is clean and the verification is honest: optimal N^(p+1) spatial convergence on the analytical slab test, Reed and anisotropic tests agree with OpenMC within a couple percent, and the fusion blanket benchmark matches within 10% for E > 10 eV, with tritium breeding within 1.5%. That is real evidence the discretization works.\n\nSoft spots, in proportion. The abstract says \"quickly and accurately assessing the neutron response of a fusion reactor, even in three-dimensional geometry.\" The evidence does not support that yet. The only 3D benchmark is a slab with two rectangular void cutouts; it does not exercise curved surfaces, toroidal or helical geometry, or the unstructured-mesh flexibility that motivates the method. There is no wall-clock comparison; the speed claim is one sentence and the conclusion explicitly defers both complex-geometry benchmarking and timing to a future paper. The low-energy (E < 10 eV) discrepancies are acknowledged, and the upscatter assumption is tested directly, which is good practice, but those discrepancies are unresolved for design-relevant thermal fluxes. The problem-specific cross sections come from OpenMC, which is fine for benchmarking but means the good blanket agreement is partly inherited from the reference code. No code or data is shipped, so reproduction is impossible without contacting the authors.\n\nNone of this is fatal. The authors are candid about the limits—the conclusion says exactly what I would want it to say. The mismatch is between the abstract and the evidence, not between the paper and itself. The method is a plausible middle-ground between reduced models and Monte Carlo for early-stage stellarator design, and the numerical foundation is solid.\n\nWho this is for: anyone building deterministic neutronics for fusion, or evaluating tools for blanket design. It deserves a serious referee. Recommend sending to peer review with a request that the authors either add a real 3D geometry test or revise the abstract to match what is actually demonstrated.","headline":"Solid methods paper with honest benchmarks; the abstract overclaims the 3D fusion capability, which is only demonstrated on a slab with rectangular cutouts and no timing comparison, but the core derivation and verification are worth a referee.","tokens_in":23328,"tokens_out":1933,"would_cite":true,"duration_ms":17884,"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":"A deterministic transport method combining arbitrary-order discontinuous Galerkin spatial discretization, discrete ordinates, multigroup energy groups, and matrix-free iterative solvers delivers fusion blanket neutron fluxes within 10% of…","keywords":["discontinuous Galerkin","discrete ordinates","multigroup neutron transport","fusion blanket","tritium breeding ratio","matrix-free iterative solvers","unstructured mesh","neutron transport"],"falsifier":"Run the method on a well-moderated problem where most of the scalar flux lies below $1$ eV at material temperatures near $1000$ K, and compare the sub-eV flux and a neutronically sensitive response (such as an absorption rate in a detector nuclide) against a continuous-energy Monte Carlo reference; if the disagreement exceeds the 10% margin established in the blanket benchmark, the central accuracy claim is limited to energies where upscatter is negligible.","tokens_in":1852,"feed_emoji":"☢️","tokens_out":1792,"duration_ms":67727,"temperature":0.7,"pith_summary":"The paper introduces a deterministic neutron transport solver intended to fill the gap between slow, high-fidelity Monte Carlo simulations and fast but drastically reduced models used in early fusion design. It solves the six-dimensional transport equation on unstructured meshes using arbitrary-order discontinuous Galerkin spatial discretization, discrete-ordinates angular discretization, multigroup energy discretization, arbitrary-order anisotropic scattering, and matrix-free iterative solvers. The claim is that this combination makes three-dimensional neutron-response calculations fast enough for iterative design while staying close to Monte Carlo accuracy, demonstrated in a breeding blanket benchmark with scalar flux within 10% for $E>10$ eV and tritium breeding within 1.5% of a continuous-energy Monte Carlo reference (1% with problem-specific cross sections). Verification against analytic solutions and literature scattering tests shows optimal spatial convergence orders in one, two, and three dimensions. A sympathetic reader would take the central claim to be that this method provides a practical deterministic alternative for neutronic design assessment in fusion.","feed_headline":"Deterministic neutronics resolves 3D fusion blankets within 10 percent","feed_subtitle":"Blanket fluxes and tritium breeding track Monte Carlo references, with speed aimed at design-loop use.","key_machinery":"The load-bearing machinery is the discontinuous Galerkin spatial discretization with an upwind numerical flux, which makes the spatial sweep a topological ordering of a directed acyclic graph: each element's solution depends only on its inflow neighbours, so elements are solved one by one with element-local matrices of size $p\\times p$ instead of one global system. The same structure is then accelerated by a simplex simplification in which the volume, flux, and edge matrices are evaluated once on a reference element, so each element solve reduces to matrix additions and matrix-vector products. Scattering-source convergence is handled by matrix-free iterative solvers acting on spherical-harmonic moments of the angular flux, whose dimension is far smaller than the number of discrete angles, and the no-upscatter assumption makes the multigroup coupling lower-triangular so energy groups are solved sequentially from the highest to the lowest energy.","core_discovery":"The paper's central claim is that a particular combination of existing discretizations produces a neutron transport scheme that is simultaneously arbitrary-order, unstructured, and fast enough for design-loop use: discontinuous Galerkin in space with an upwind numerical flux, discrete ordinates in angle, a multigroup energy structure solved from high to low energy, arbitrary-order anisotropic scattering, and matrix-free Krylov iterative solvers for the within-group scattering source. The authors derive the single-element transport sweep on straight-sided convex elements, simplify it for simplexes so that element matrices are precomputed and no integrals are needed during sweeps, and then verify the implementation against an analytic solution, isotropic and anisotropic scattering tests, and a fusion-relevant breeding blanket benchmark in both one- and three-dimensional geometries. The blanket test shows scalar flux agreement within 10% for energies above $10$ eV, tritium breeding 1.5% lower than the Monte Carlo reference with standard cross sections and 1% lower with problem-specific cross sections, and qualitative agreement across five orders of magnitude of flux and twelve orders of magnitude of energy spectrum.","pith_inferences":["A direct but unstated consequence is that removing the no-upscatter assumption with outer iterations over the lowest energy groups would likely shrink the observed $E<10$ eV edge discrepancies, since the paper's own comparison attributes part of that gap to neglected group-to-group upscatter.","Not stated in the paper but a natural next test: the method's speed advantage should be largest in strongly three-dimensional, curved geometries such as stellarator blankets, where Monte Carlo sampling and CAD faceting are hardest, so a direct head-to-head wall-clock comparison in such a geometry would sharpen the design-cycle claim.","The paper lists differentiable solutions only as a future possibility, but because the element matrices and sweep order are fixed and cheap, a shape-optimization loop that differentiates tritium breeding with respect to blanket geometry appears to be a plausible extension of the same machinery.","An untested but direct generalization is to include upscatter by iterating the energy-group loop rather than solving it in a single downward pass; the paper describes this cost but does not quantify it, so a benchmark with a thermal-energy design quantity would show whether the trade-off is acceptable."],"forward_implications":["Blanket scalar fluxes above $10$ eV and tritium breeding ratios can be obtained from a deterministic solve in one, two, and three dimensions without running millions of Monte Carlo histories.","Because the mesh is unstructured and the sweep is element-local, the solver can be applied to curved, component-level, or simplified full-reactor geometries and coupled to other engineering design codes.","Problem-specific multigroup cross sections generated once from a Monte Carlo run improve agreement significantly and can be reused for nearby design variants, which is useful in design optimization.","The full angular flux distribution is available from the deterministic solve rather than only tally-based results, so high-fluence or neutron-penetration regions can be identified directly during design.","The matrix-free formulation keeps memory use low because the full transport matrix is never formed; only the action of the operator on a moment vector is needed for GMRES- or BiCGSTAB-style iterations."],"supporting_citations":[{"why":"Supplies the standard multigroup and discrete-ordinates phase-space discretization on which the scheme is built.","marker":"[8]"},{"why":"Provides the spatial sweep and matrix-free iterative-solver approach that the paper adapts and extends to arbitrary-order discontinuous Galerkin discretization.","marker":"[9]"},{"why":"Earlier deterministic fusion neutronics work cited for the no-upscatter assumption and for the fusion application context.","marker":"[15]"},{"why":"Supplies the nodal discontinuous Galerkin framework and the optimal convergence theory used for verification.","marker":"[22]"},{"why":"The Monte-Carlo code used to generate reference solutions and problem-specific multigroup cross sections for the benchmarks.","marker":"[33]"},{"why":"Describes the method for generating multigroup cross sections from Monte-Carlo particle histories, which the paper uses for the problem-specific data.","marker":"[21]"},{"why":"The nuclear data library through which standard multigroup cross sections are obtained for the blanket benchmark.","marker":"[32]"},{"why":"Earlier work providing an anisotropic-scattering benchmark that the paper reproduces with new reference data.","marker":"[11]"},{"why":"Source of the anisotropic multigroup scattering test data used in the second literature verification.","marker":"[36]"},{"why":"Provides the layered breeding-blanket geometry and materials used for the final fusion-relevant benchmark.","marker":"[38]"}],"fun_headline_variants":["Fusion blanket neutronics: 10% accuracy, design-loop speed","3D neutron transport for fusion blankets: fast and close to MC","DG-neutronics model validated for fusion blanket design","New deterministic neutronics code speeds fusion design iterations","DG + Sn neutronics: fusion blankets in design loop"],"cache_read_input_tokens":25472,"weakest_assumption_plain":"The load-bearing premise is that neutrons never gain energy in scattering events, so group-to-group upscatter is neglected; the paper acknowledges this breaks down below about $10$ eV, and the low-energy blanket-edge flux is exactly where benchmark agreement degrades.","fun_headline_variants_meta":{"raw":{"variants":["Fusion blanket neutronics: 10% accuracy, design-loop speed","3D neutron transport for fusion blankets: fast and close to MC","DG-neutronics model validated for fusion blanket design","New deterministic neutronics code speeds fusion design iterations","DG + Sn neutronics: fusion blankets in design loop"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001362,"raw_usage":{"total_tokens":5505,"prompt_tokens":904,"completion_tokens":4601,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":520,"completion_tokens_details":{"reasoning_tokens":4518}},"tokens_in":520,"tokens_out":4601,"duration_ms":31448,"temperature":1.0,"reasoning_tokens":4518,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T13:11:33.718344+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the method on a well-moderated problem where most of the scalar flux lies below $1$ eV at material temperatures near $1000$ K, and compare the sub-eV flux and a neutronically sensitive response (such as an absorption rate in a detector nuclide) against a continuous-energy Monte Carlo reference; if the disagreement exceeds the 10% margin established in the blanket benchmark, the central accuracy claim is limited to energies where upscatter is negligible.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the standard multigroup and discrete-ordinates phase-space discretization on which the scheme is built."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the spatial sweep and matrix-free iterative-solver approach that the paper adapts and extends to arbitrary-order discontinuous Galerkin discretization."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Earlier deterministic fusion neutronics work cited for the no-upscatter assumption and for the fusion application context."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the nodal discontinuous Galerkin framework and the optimal convergence theory used for verification."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The Monte-Carlo code used to generate reference solutions and problem-specific multigroup cross sections for the benchmarks."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Describes the method for generating multigroup cross sections from Monte-Carlo particle histories, which the paper uses for the problem-specific data."},{"cited_title":"2024 Nuclear Data Sheets 193 1–78","cited_arxiv_id":null,"evidence_quote":"The nuclear data library through which standard multigroup cross sections are obtained for the blanket benchmark."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Earlier work providing an anisotropic-scattering benchmark that the paper reproduces with new reference data."},{"cited_title":"1978 Journal of Nuclear Science and Technology 15 56–71","cited_arxiv_id":null,"evidence_quote":"Source of the anisotropic multigroup scattering test data used in the second literature verification."},{"cited_title":"2017 Fusion Engineering and Design 123 47–53","cited_arxiv_id":null,"evidence_quote":"Provides the layered breeding-blanket geometry and materials used for the final fusion-relevant benchmark."}],"review_version":1}