Benchmark Supercritical Wing (BSCW)

• Benchmark Supercritical Wing (BSCW) is a standard transonic wing configuration used in aerodynamic and aeroelastic research with clearly defined geometry and operating protocols.
• It is applied in dual roles: a buffet case study for analyzing shock motion and flow separation, and a forced-motion URANS case for unsteady surface-pressure forecasting.
• Advanced numerical and machine-learning methods leveraging BSCW data enable accurate prediction of unsteady pressure fields with significant computational savings.

Searching arXiv for recent and foundational papers related to Benchmark Supercritical Wing and closely related benchmark transonic wing studies. arxiv_search.query({"^^^^^^^^13search_query13 Supercritical Wing\"^^^^^^^^13 OR all:BSCW13^^^^^^^^", "^^^^^^^^13start13 ^^^^13search_query13^^^^, "^^^^^^^^13max_results13 ^^^^13all:\13search_query13^^^^, "^^^^^^^^13sort_by13 "^^^^^^^^13submittedDate13 "^^^^^^^^13sort_order13 "^^^^^^^^13descending13 arxiv_search.query({"^^^^^^^^13search_query13 Supercritical Wing\"^^^^^^^^13all:\13all:\13 Supercritical Wing\"^^^^^^^^13all:\13 OR all:BSCW13^^^^^^^^"Benchmark Supercritical Wing\"", "^^^^^^^^13start13 ^^^^13search_query13^^^^, "^^^^^^^^13max_results13 ^^^^13all:\13search_query13^^^^, "^^^^^^^^13sort_by13 "relevance", "^^^^^^^^13sort_order13 "^^^^^^^^13descending13 arxiv_search.query({"^^^^^^^^13search_query13 instability of wing shock buffet\" OR id:(&&&^^^^13search_query13^^^^&&&)", "^^^^^^^^13start13 ^^^^13search_query13^^^^, "^^^^^^^^13max_results13 ^^^^13sort_by13^^^^, "^^^^^^^^13sort_by13 "relevance", "^^^^^^^^13sort_order13 "^^^^^^^^13descending13 Benchmark Supercritical Wing (BSCW) is a standard benchmark supercritical-wing configuration used in transonic aerodynamic and aeroelastic research. In the literature considered here, it appears in two closely related benchmark roles. One is the unswept finite-wing configuration used in NASA Aeroelastic Prediction Workshop-^^^^13 OR all:BSCW13^^^^ (AePW-^^^^13 OR all:BSCW13^^^^) Optional Test Case-^^^^13start13^^^^a to study transonic buffet, shock-foot motion, and three-dimensional separated-flow topology. The other is the AIAA Aeroelastic Prediction Workshop transonic rigid semi-span wing used to generate forced-motion unsteady Reynolds-averaged Navier–Stokes (URANS) data for forecasting time-resolved surface pressure distributions on an unstructured mesh (&&&^^^^13all:\13^^^^&&&, &&&^^^^13 OR all:BSCW13^^^^&&&).

^^^^13all:\13^^^^. Benchmark identity and research role

BSCW is treated as a benchmark rather than as a generic supercritical wing. In the buffet study, it is identified specifically with the AePW-^^^^13 OR all:BSCW13^^^^ configuration chosen because it exhibits strong shock waves and flow separation. In the forecasting study, it is described as a transonic rigid semi-span wing with a rectangular planform and a supercritical airfoil profile, framed as a standard benchmark for flutter-oriented studies (&&&^^^^13all:\13^^^^&&&, &&&^^^^13 OR all:BSCW13^^^^&&&).

The benchmark is important because it occupies an intermediate position between classical two-dimensional supercritical-airfoil studies and swept transport-wing configurations. The unswept finite-wing setup isolates finite-span three-dimensionality without sweep-induced complications typical of civil-aircraft wings, while still exhibiting genuinely three-dimensional separated-flow structure and low-frequency transonic unsteadiness (&&&^^^^13all:\13^^^^&&&).

Benchmark use	Main purpose	Representative conditions
AePW-^^^^13 OR all:BSCW13^^^^ Optional Test Case-^^^^13start13^^^^a	Transonic buffet and surface-topology analysis	PRESERVED_PLACEHOLDER_^^^^13search_query13^^^^, PRESERVED_PLACEHOLDER_^^^^13all:\13^^^^
AIAA Aeroelastic Prediction Workshop forced-motion case	Unsteady surface-pressure forecasting under prescribed pitch/plunge	PRESERVED_PLACEHOLDER_^^^^13 OR all:BSCW13^^^^, PRESERVED_PLACEHOLDER_^^^^13start13^^^^, PRESERVED_PLACEHOLDER_^^^^13max_results13^^^^

A recurring implication is that “BSCW” denotes a benchmark family of well-defined configurations and protocols rather than a single universal operating point. This suggests that comparisons across BSCW studies require attention to the exact workshop framing, flow conditions, and whether the problem is steady, buffeting, or forced-motion unsteady.

^^^^13 OR all:BSCW13^^^^. Geometry and canonical operating conditions

For the AePW-^^^^13 OR all:BSCW13^^^^ buffet study, the BSCW is a uniform wing with a rectangular planform, unswept geometry, aspect ratio PRESERVED_PLACEHOLDER_^^^^13sort_by13^^^^, and NASA SC(^^^^13 OR all:BSCW13^^^^)-^^^^13search_query13max_results13all:\13max_results13^^^^ second-generation supercritical airfoil section. The reported design lift coefficient is PRESERVED_PLACEHOLDER_^^^^13submittedDate13^^^^, the thickness-to-chord ratio is PRESERVED_PLACEHOLDER_^^^^13sort_order13^^^^, and the chord used in the Strouhal definition is PRESERVED_PLACEHOLDER_^^^^13descending13^^^^ inches. The wing is mounted in a wind-tunnel-like arrangement on a splitter plate, modeled numerically as an inviscid wall plane (&&&^^^^13all:\13^^^^&&&).

For the forced-motion URANS dataset, the reported reference quantities are a reference chord PRESERVED_PLACEHOLDER_^^^^13search_query13^^^^, surface area PRESERVED_PLACEHOLDER_^^^^13all:\13search_query13^^^^, and a pitch axis about PRESERVED_PLACEHOLDER_^^^^13all:\13all:\13^^^^ chord. The wing is mounted on a support with two kinematic degrees of freedom, pitch PRESERVED_PLACEHOLDER_^^^^13all:\13 OR all:BSCW13^^^^ and plunge PRESERVED_PLACEHOLDER_^^^^13all:\13start13^^^^, but the study does not solve a coupled aeroelastic problem; it prescribes time-dependent motions and predicts the resulting pressure distributions (&&&^^^^13 OR all:BSCW13^^^^&&&).

The two main BSCW operating protocols differ materially. The buffet study uses PRESERVED_PLACEHOLDER_^^^^13all:\13max_results13^^^^, PRESERVED_PLACEHOLDER_^^^^13all:\13sort_by13^^^^, and angles of attack PRESERVED_PLACEHOLDER_^^^^13all:\13submittedDate13^^^^. It reports unsteady buffet for all these angles except PRESERVED_PLACEHOLDER_^^^^13all:\13sort_order13^^^^, where the URANS solution converges to steady flow, so buffet offset lies between PRESERVED_PLACEHOLDER_^^^^13all:\13descending13^^^^ and PRESERVED_PLACEHOLDER_^^^^13all:\13search_query13^^^^, while buffet onset is inferred to be below PRESERVED_PLACEHOLDER_^^^^13 OR all:BSCW13search_query13^^^^ (&&&^^^^13all:\13^^^^&&&). By contrast, the forced-motion study fixes the initial angle of attack at PRESERVED_PLACEHOLDER_^^^^13 OR all:BSCW13all:\13^^^^ and generates data from ^^^^13all:\13 OR all:BSCW13^^^^ imposed pitch/plunge simulations spanning damped Schroeder-phased harmonic, undamped Schroeder-phased harmonic, and single-harmonic signals (&&&^^^^13 OR all:BSCW13^^^^&&&).

^^^^13start13^^^^. Buffet phenomenology on the unswept finite wing

The buffet study characterizes BSCW unsteadiness as low-frequency transonic buffet with dominant reduced frequencies of order PRESERVED_PLACEHOLDER_^^^^13 OR all:BSCW13 OR all:BSCW13^^^^, using

PRESERVED_PLACEHOLDER_^^^^13 OR all:BSCW13start13^^^^

The reported dominant values are PRESERVED_PLACEHOLDER_^^^^13 OR all:BSCW13max_results13^^^^ at PRESERVED_PLACEHOLDER_^^^^13 OR all:BSCW13sort_by13^^^^, PRESERVED_PLACEHOLDER_^^^^13 OR all:BSCW13submittedDate13^^^^ at PRESERVED_PLACEHOLDER_^^^^13 OR all:BSCW13sort_order13^^^^, PRESERVED_PLACEHOLDER_^^^^13 OR all:BSCW13descending13^^^^ at PRESERVED_PLACEHOLDER_^^^^13 OR all:BSCW13search_query13^^^^, PRESERVED_PLACEHOLDER_^^^^13start13search_query13^^^^ at PRESERVED_PLACEHOLDER_^^^^13start13all:\13^^^^, and PRESERVED_PLACEHOLDER_^^^^13start13 OR all:BSCW13^^^^ at PRESERVED_PLACEHOLDER_^^^^13start13start13^^^^. A notable result is that buffet PRESERVED_PLACEHOLDER_^^^^13start13max_results13^^^^ decreases as angle of attack increases, opposite to trends often reported in two-dimensional buffet studies (&&&^^^^13all:\13^^^^&&&).

Shock motion and separated-flow topology are coupled. On the suction surface, the mean shock moves toward the leading edge as angle of attack increases; on the pressure surface, it moves toward the trailing edge. The separation region therefore increases on the suction surface and decreases on the pressure surface. Shock-foot excursion amplitudes are generally between PRESERVED_PLACEHOLDER_^^^^13start13sort_by13^^^^ and PRESERVED_PLACEHOLDER_^^^^13start13submittedDate13^^^^ of chord and are reported to be much smaller than two-dimensional buffet amplitudes (&&&^^^^13all:\13^^^^&&&).

The central physical interpretation is topological. A buffet cell is identified with a curvature or waviness of the separation line, approximately the locus of the shock foot along the span. The paper attributes the formation and propagation of buffet cells to pairs of contra-rotating unstable foci embedded within the separated region. One or multiple such pairs can create one or multiple buffet cells. In this formulation, buffet cells are not merely pressure-wave artifacts; they are surface manifestations of a specific three-dimensional critical-point topology (&&&^^^^13all:\13^^^^&&&).

A striking feature of this BSCW case is that the dominant hydrodynamic propagation is primarily inboard, toward the root, rather than the outboard propagation often emphasized for swept wings. The study reports that pressure-wave propagation, buffet-cell propagation, and the self-induced motion of unstable foci occur together and at nearly the same spanwise wavelength and speed. At PRESERVED_PLACEHOLDER_^^^^13start13sort_order13^^^^, identified as the special BSCW case, both surfaces participate, the spectrum is broadband, and the suction and pressure surfaces carry different dominant frequencies: PRESERVED_PLACEHOLDER_^^^^13start13descending13^^^^ on the suction surface and PRESERVED_PLACEHOLDER_^^^^13start13search_query13^^^^ on the pressure surface (&&&^^^^13all:\13^^^^&&&).

The distribution of buffet activity across the two surfaces varies with angle of attack. At PRESERVED_PLACEHOLDER_^^^^13max_results13search_query13^^^^ and PRESERVED_PLACEHOLDER_^^^^13max_results13all:\13^^^^, buffet cells are mainly seen on the pressure surface. At PRESERVED_PLACEHOLDER_^^^^13max_results13 OR all:BSCW13^^^^, the suction surface begins to develop a near-root buffet-cell-like structure. At PRESERVED_PLACEHOLDER_^^^^13max_results13start13^^^^, both surfaces support propagating buffet cells. At PRESERVED_PLACEHOLDER_^^^^13max_results13max_results13^^^^, buffet-cell propagation is strongest on the suction surface, while the pressure surface becomes partial or irregular. At PRESERVED_PLACEHOLDER_^^^^13max_results13sort_by13^^^^, no buffet and no corresponding focus-pair topology are observed (&&&^^^^13all:\13^^^^&&&).

^^^^13max_results13^^^^. Diagnostic formulations and numerical methodology

The distinguishing analysis framework for BSCW buffet combines URANS with surface-topology diagnostics. The solver is CFL^^^^13start13^^^^D v^^^^13submittedDate13^^^^.^^^^13sort_order13^^^^ with the Spalart–Allmaras turbulence model, a structured finite-volume method, Roe second-order upwind flux-difference splitting, third-order-limited interpolation for inviscid terms, second-order central differencing for viscous and heat terms, second-order backward Euler in time, and dual-time stepping. Final results use the fine AePW-^^^^13 OR all:BSCW13^^^^ grid with ^^^^13all:\13submittedDate13^^^^.^^^^13search_query13^^^^ million nodes, wing surface resolution PRESERVED_PLACEHOLDER_^^^^13max_results13submittedDate13^^^^ in chord PRESERVED_PLACEHOLDER_^^^^13max_results13sort_order13^^^^ span, a hemispherical far field at PRESERVED_PLACEHOLDER_^^^^13max_results13descending13^^^^, and wall-normal resolution PRESERVED_PLACEHOLDER_^^^^13max_results13search_query13^^^^, corresponding to first-cell height PRESERVED_PLACEHOLDER_^^^^13sort_by13search_query13^^^^ (&&&^^^^13all:\13^^^^&&&).

Surface topology is expressed through the skin-friction vector

PRESERVED_PLACEHOLDER_^^^^13sort_by13all:\13^^^^

with skin-friction lines satisfying

PRESERVED_PLACEHOLDER_^^^^13sort_by13 OR all:BSCW13^^^^

Critical points are locations where the skin-friction vector vanishes, and the topological constraint for a wing mounted on a wall is

PRESERVED_PLACEHOLDER_^^^^13sort_by13start13^^^^

where PRESERVED_PLACEHOLDER_^^^^13sort_by13max_results13^^^^ is the number of nodes, PRESERVED_PLACEHOLDER_^^^^13sort_by13sort_by13^^^^ the number of foci, and PRESERVED_PLACEHOLDER_^^^^13sort_by13submittedDate13^^^^ the number of saddles. The study states that this relation is satisfied for every fully developed instantaneous topology identified on the BSCW surfaces (&&&^^^^13all:\13^^^^&&&).

Pressure-disturbance propagation is analyzed by two-point cross-correlation of pressure-coefficient fluctuations, and phase velocity is extracted from the slope of correlation maxima in PRESERVED_PLACEHOLDER_^^^^13sort_by13sort_order13^^^^ space. The study distinguishes hydrodynamic waves, of order PRESERVED_PLACEHOLDER_^^^^13sort_by13descending13^^^^ or PRESERVED_PLACEHOLDER_^^^^13sort_by13search_query13^^^^, from faster acoustic waves of order PRESERVED_PLACEHOLDER_^^^^13submittedDate13search_query13^^^^ or more. It focuses on hydrodynamic waves because these correlate with buffet-cell motion and critical-point motion. Frequency content is estimated using a Burg autoregressive method with signal length PRESERVED_PLACEHOLDER_^^^^13submittedDate13all:\13^^^^ s and ^^^^13max_results13sort_by13search_query13^^^^ samples (&&&^^^^13all:\13^^^^&&&).

In the forced-motion benchmark usage, the reference data are generated with SU^^^^13 OR all:BSCW13^^^^ v^^^^13sort_order13^^^^.^^^^13sort_by13 solving the URANS equations with the Spalart–Allmaras one-equation turbulence model. The unstructured grid contains PRESERVED_PLACEHOLDER_^^^^13submittedDate13 OR all:BSCW13^^^^ elements, of which ^^^^13descending13submittedDate13^^^^,^^^^13descending13max_results13search_query13^^^^ are surface elements, with PRESERVED_PLACEHOLDER_^^^^13submittedDate13start13^^^^ and a farfield extending ^^^^13all:\13search_query13search_query13^^^^ chord lengths from the solid wall. The URANS time step is PRESERVED_PLACEHOLDER_^^^^13submittedDate13max_results13^^^^ over a total simulation time of ^^^^13 OR all:BSCW13^^^^ s, later downsampled to PRESERVED_PLACEHOLDER_^^^^13submittedDate13sort_by13^^^^ for machine learning (&&&^^^^13 OR all:BSCW13^^^^&&&).

^^^^13sort_by13^^^^. BSCW as a reduced-order and machine-learning benchmark

BSCW has also been used as the sole aerodynamic application for graph-based forecasting of unsteady transonic surface-pressure fields on an unstructured wing mesh. In that formulation, the prediction target is the full surface pressure coefficient field PRESERVED_PLACEHOLDER_^^^^13submittedDate13submittedDate13^^^^ over all wing-surface graph nodes, while PRESERVED_PLACEHOLDER_^^^^13submittedDate13sort_order13^^^^ and PRESERVED_PLACEHOLDER_^^^^13submittedDate13descending13^^^^ are derived for assessment rather than used as primary targets (&&&^^^^13 OR all:BSCW13^^^^&&&).

The proposed framework, GST GraphNet, combines a pre-trained graph autoencoder, a graph-based temporal model in latent space, and a decoder that reconstructs full-surface PRESERVED_PLACEHOLDER_^^^^13submittedDate13search_query13^^^^. Each wing-surface grid point is treated as a graph node; node features include spatial coordinates PRESERVED_PLACEHOLDER_^^^^13sort_order13search_query13^^^^, pitch kinematics PRESERVED_PLACEHOLDER_^^^^13sort_order13all:\13^^^^, plunge kinematics PRESERVED_PLACEHOLDER_^^^^13sort_order13 OR all:BSCW13^^^^, and previous PRESERVED_PLACEHOLDER_^^^^13sort_order13start13^^^^ values in the autoregressive variant. The graph convolution uses the Kipf–Welling propagation rule

PRESERVED_PLACEHOLDER_^^^^13sort_order13max_results13^^^^

and the framework compares GRU, LSTM, attention, and STGCN temporal layers (&&&^^^^13 OR all:BSCW13^^^^&&&).

The practical conclusion is architectural rather than merely numerical. Feedforward forecasting is more stable than ARMAX because ARMAX accumulates error once it switches from ground-truth to self-predicted pressure histories. Among temporal models, STGCN is the best overall temporal layer, with LSTM close behind. On the two validation signals, feedforward STGCN gives RMSE PRESERVED_PLACEHOLDER_^^^^13sort_order13sort_by13^^^^ and PRESERVED_PLACEHOLDER_^^^^13sort_order13submittedDate13^^^^, while feedforward LSTM gives MAPE PRESERVED_PLACEHOLDER_^^^^13sort_order13sort_order13^^^^ and PRESERVED_PLACEHOLDER_^^^^13sort_order13descending13^^^^ and PRESERVED_PLACEHOLDER_^^^^13sort_order13search_query13^^^^ PRESERVED_PLACEHOLDER_^^^^13descending13search_query13^^^^ and PRESERVED_PLACEHOLDER_^^^^13descending13all:\13^^^^ for the damped Schroeder and single-harmonic cases, respectively. The ARMAX versions are markedly worse; for example, ARMAX STGCN gives RMSE PRESERVED_PLACEHOLDER_^^^^13descending13 OR all:BSCW13^^^^ and PRESERVED_PLACEHOLDER_^^^^13descending13start13^^^^ and PRESERVED_PLACEHOLDER_^^^^13descending13max_results13^^^^ PRESERVED_PLACEHOLDER_^^^^13descending13sort_by13^^^^ and PRESERVED_PLACEHOLDER_^^^^13descending13submittedDate13^^^^ on the same two validation signals (&&&^^^^13 OR all:BSCW13^^^^&&&).

The computational contrast is explicit. One unsteady BSCW CFD simulation requires about ^^^^13submittedDate13^^^^,^^^^13search_query13search_query13search_query13^^^^ CPU hours, and all ^^^^13all:\13 OR all:BSCW13^^^^ dataset-generation runs require about ^^^^13sort_order13sort_by13^^^^,^^^^13search_query13search_query13search_query13^^^^ CPU hours. By contrast, feedforward or ARMAX inference requires ^^^^13search_query13^^^^.^^^^13search_query13start13^^^^ GPU hours per sample, roughly two minutes on an NVIDIA RTX A^^^^13max_results13search_query13search_query13search_query13^^^^ GPU, and the paper summarizes the reduction as over ^^^^13search_query13search_query13^^^^% computational savings relative to high-fidelity CFD (&&&^^^^13 OR all:BSCW13^^^^&&&).

^^^^13submittedDate13^^^^. Interpretive boundaries and common misconceptions

A common misconception is that BSCW denotes a single, fixed transonic test case. The cited literature shows instead that the benchmark is used under distinct protocols: an AePW-^^^^13 OR all:BSCW13^^^^ unswept finite-wing buffet problem at PRESERVED_PLACEHOLDER_^^^^13descending13sort_order13^^^^ and a forced-motion URANS pressure-forecasting problem at PRESERVED_PLACEHOLDER_^^^^13descending13descending13^^^^. The benchmark identity is stable, but the physical questions, excitation mechanisms, and observables differ (&&&^^^^13all:\13^^^^&&&, &&&^^^^13 OR all:BSCW13^^^^&&&).

A second misconception is that BSCW should be understood only through shock motion or only through modal pressure analysis. The buffet study argues for a surface-topology-driven interpretation in which pairs of contra-rotating unstable foci, saddles, and nodes organize the separated region and generate buffet-cell motion. The forecasting study, by contrast, treats BSCW as a high-dimensional unsteady pressure-forecasting benchmark on an unstructured mesh. These are complementary rather than contradictory views: one is mechanistic, the other is reduced-order and predictive (&&&^^^^13all:\13^^^^&&&, &&&^^^^13 OR all:BSCW13^^^^&&&).

The literature also imposes clear limits on generalization. For the buffet study, conclusions are specific to an unswept, rectangular, low-aspect-ratio finite wing at PRESERVED_PLACEHOLDER_^^^^13descending13search_query13^^^^, PRESERVED_PLACEHOLDER_^^^^13search_query13search_query13^^^^, under URANS with the Spalart–Allmaras model, and the authors explicitly acknowledge that topology changes with angle of attack, Mach number, and Reynolds number. Buffet onset is not pinned down precisely; it is inferred to be below PRESERVED_PLACEHOLDER_^^^^13search_query13all:\13^^^^, whereas buffet offset is bracketed between PRESERVED_PLACEHOLDER_^^^^13search_query13 OR all:BSCW13^^^^ and PRESERVED_PLACEHOLDER_^^^^13search_query13start13^^^^ (&&&^^^^13all:\13^^^^&&&). For the forecasting study, validation is confined to the BSCW setup and prescribed motions around the baseline transonic condition, and the hardest errors remain in leading-edge, shock, and separation regions (&&&^^^^13 OR all:BSCW13^^^^&&&).

^^^^13sort_order13^^^^. Relation to the broader supercritical-wing benchmark ecosystem

BSCW sits within a wider landscape of transonic benchmark configurations, but that broader literature must be separated carefully into direct and indirect relevance. A global-instability study of wing shock buffet analyzes the NASA Common Research Model rather than BSCW. It nevertheless matters because it demonstrates that a realistic public high-PRESERVED_PLACEHOLDER_^^^^13search_query13max_results13^^^^ swept supercritical wing can be treated by global linear stability analysis and that incipient three-dimensional wing shock buffet can be governed by a single unstable global mode. The connection to BSCW is therefore methodological and physical, not configurational (&&&^^^^13search_query13^^^^&&&).

Machine-learning work on transonic wings likewise often has strong methodological relevance without being a direct BSCW study. Transfer learning from two-dimensional supercritical airfoils to three-dimensional swept wings uses a family of simplified CRM-based wing-body configurations rather than canonical BSCW geometry, but it shows that sectionwise PRESERVED_PLACEHOLDER_^^^^13search_query13sort_by13^^^^ surrogates and inverse models can achieve useful performance with approximately ^^^^13sort_by13search_query13search_query13^^^^ wing samples after embedding simple swept theory (&&&^^^^13start13search_query13^^^^&&&). The SuperWing dataset introduces ^^^^13max_results13^^^^,^^^^13 OR all:BSCW13start13search_query13^^^^ parameterized wing geometries and ^^^^13 OR all:BSCW13descending13^^^^,^^^^13descending13sort_by13submittedDate13^^^^ RANS flow-field solutions and demonstrates zero-shot transfer to DLR-F^^^^13submittedDate13^^^^ and NASA CRM, but BSCW is not included as a geometry and is not directly evaluated (&&&^^^^13start13all:\13^^^^&&&).

Two-dimensional supercritical-airfoil methodology is also relevant in a non-benchmark sense. Output-space sampling of pressure-distribution features develops feature descriptors such as shock location PRESERVED_PLACEHOLDER_^^^^13search_query13submittedDate13^^^^, wall Mach number immediately upstream of the shock PRESERVED_PLACEHOLDER_^^^^13search_query13sort_order13^^^^, suction-peak wall Mach number PRESERVED_PLACEHOLDER_^^^^13search_query13descending13^^^^, and a modified Korn-like relation

PRESERVED_PLACEHOLDER_^^^^13search_query13search_query13^^^^

This does not constitute a BSCW result, but it provides a section-based language for analyzing supercritical pressure distributions, drag divergence, and drag creep that is transferable to benchmark post-processing workflows (&&&^^^^13start13 OR all:BSCW13^^^^&&&).

Taken together, these studies place BSCW in a dual role. It is a direct benchmark for unswept finite-wing transonic buffet and for unsteady pressure-field forecasting under prescribed motion, and it is also a reference point against which broader benchmark-wing, reduced-order, and data-driven methods can be interpreted. Its continuing value lies in that combination of physical specificity and methodological portability.