Reconstruct NeuralFoil's surface pressure from edge velocity in arc length

CHANGELOG.md

@@ -1,5 +1,23 @@
 # Changelog
 
+## Unreleased
+
+### Fixed
+- The NeuralFoil surface pressure is now reconstructed from the predicted edge
+  velocities in arc length, not by interpolating `Cp` in chord fraction.
+  NeuralFoil samples at the cell centres of a uniform grid, so it reports nothing
+  over the first and last `1/2N` of chord; the old code extrapolated `Cp` off the
+  end of each surface independently. Through a stagnation point `ue` is linear in
+  arc length while `Cp` is quadratic, so that extrapolated a parabola through its
+  own turning point: on an SK100 section it put `Cp = -1.60` at the leading edge,
+  where it has to approach `+1`, and the two surfaces disagreed at the trailing
+  edge in violation of the Kutta condition. Signing the lower surface negative
+  makes both surfaces one continuous curve through stagnation, so the nose is
+  interpolated rather than extrapolated, and the trailing edge takes one speed for
+  both surfaces. Integrating that section's surface traction now recovers 98% of
+  NeuralFoil's own reported drag where it previously came out with the wrong sign.
+  `neuralfoil_section` returns `ue_upper`/`ue_lower` alongside the pressures.
+
 ## VortexStepMethod v4.2.0 2026-08-25
 
 ### Added

docs/src/private_functions.md

@@ -175,6 +175,10 @@ write_aero_matrix
 write_node_table
 flat_plate_cf
 neuralfoil_contour_solution
+contour_arc
+arc_at_chord
+trailing_edge_speed
+velocity_knots
 fill_node_nans!
 ```
 

src/airfoil_aero/airfoil_solvers/neuralfoil_solver.jl

@@ -24,32 +24,120 @@ end
     analyze_sweep(solver::NeuralFoilSolver, def, alpha_range, Re) -> Vector{SectionSolution}
 
 Evaluate all angles (radians) in one vectorized NeuralFoil call on the deformed
-Kulfan parameters, then assemble a single per-node `cp` on the deformed contour nodes
-(`def.x`, `def.y`) from NeuralFoil's separate upper/lower surface pressures. `cf` is a
-flat-plate closure ([`flat_plate_cf`](@ref)), NeuralFoil not exposing skin friction.
+Kulfan parameters, then assemble a per-node `cp` on the deformed contour nodes
+(`def.x`, `def.y`) from the predicted edge velocities
+([`neuralfoil_contour_solution`](@ref)). `cf` is a flat-plate closure
+([`flat_plate_cf`](@ref)), NeuralFoil not exposing skin friction.
 """
 function analyze_sweep(solver::NeuralFoilSolver, def::DeformedSection, alpha_range, Re)
     res = neuralfoil_section(def.kulfan, rad2deg.(collect(alpha_range)), Re;
         model_size=solver.model_size, weights_dir=solver.weights_dir,
         n_crit=solver.n_crit, xtr_upper=solver.xtr_upper, xtr_lower=solver.xtr_lower)
     x, y = collect(float.(def.x)), collect(float.(def.y))
     le = argmin(x)
+    arc = contour_arc(x, y, le)
     cf = [flat_plate_cf(clamp(xk, 0.0, 1.0), Re) for xk in x]
-    return [neuralfoil_contour_solution(alpha_range[i], res, i, x, y, le, cf)
+    return [neuralfoil_contour_solution(alpha_range[i], res, i, x, y, le, arc, cf)
             for i in eachindex(alpha_range)]
 end
 
 """
-    neuralfoil_contour_solution(alpha, res, i, x, y, le, cf) -> SectionSolution
+    contour_arc(x, y, le) -> Vector
+
+Signed arc length of every contour node from the leading edge node `le`: positive
+along the upper surface toward the trailing edge, negative along the lower. The
+natural coordinate across a blunt nose, where a small chordwise step is a long one
+along the skin.
+"""
+function contour_arc(x, y, le)
+    arc = zeros(Float64, length(x))
+    for k in (le - 1):-1:1
+        arc[k] = arc[k + 1] + hypot(x[k] - x[k + 1], y[k] - y[k + 1])
+    end
+    for k in (le + 1):length(x)
+        arc[k] = arc[k - 1] - hypot(x[k] - x[k - 1], y[k] - y[k - 1])
+    end
+    return arc
+end
+
+"""
+    arc_at_chord(x, arc, indices, fractions) -> Vector
+
+Signed arc length at each chord fraction, read off the contour nodes `indices` — the
+one surface the fractions belong to.
+"""
+function arc_at_chord(x, arc, indices, fractions)
+    nodes = collect(indices)
+    order = sortperm(x[nodes])
+    xs, as = x[nodes][order], arc[nodes][order]
+    return [begin
+        j = clamp(searchsortedfirst(xs, f), 2, length(xs))
+        gap = max(xs[j] - xs[j - 1], eps())
+        as[j - 1] + (f - xs[j - 1]) / gap * (as[j] - as[j - 1])
+    end for f in fractions]
+end
+
+"""
+    trailing_edge_speed(res, i, upper_arc, lower_arc, upper_te, lower_te) -> Float64
+
+One edge speed for both surfaces at the trailing edge: each surface's last two
+stations extrapolated to its own trailing-edge arc length, the two magnitudes
+averaged, so a sharp edge carries a single pressure (Kutta).
+"""
+function trailing_edge_speed(res, i, upper_arc, lower_arc, upper_te, lower_te)
+    reach(a1, a2, v1, v2, target) =
+        v2 + (target - a2) / (a2 - a1 + eps()) * (v2 - v1)
+    n = length(upper_arc)
+    n < 2 && return abs(res.ue_upper[end, i])
+    upper = reach(upper_arc[n - 1], upper_arc[n],
+                  res.ue_upper[n - 1, i], res.ue_upper[n, i], upper_te)
+    lower = reach(lower_arc[n - 1], lower_arc[n],
+                  res.ue_lower[n - 1, i], res.ue_lower[n, i], lower_te)
+    return (abs(upper) + abs(lower)) / 2
+end
+
+"""
+    velocity_knots(res, i, x, arc, le) -> (knots, values)
+
+The whole contour's edge velocity as one curve of (signed arc length, signed
+`ue/u∞`), strictly increasing in arc length.
+
+NeuralFoil reports nothing over the first and last `1/2N` of chord. Signing the lower
+surface negative joins both surfaces into one curve through the stagnation point, so
+the unsampled nose is interpolated between the innermost station on each side rather
+than extrapolated off the end of one. The stagnation point enters as its own knot,
+where `ue` interpolated linearly between those two stations reaches zero — the
+stagnation-point-flow result, `ue` being linear in arc length there.
+"""
+function velocity_knots(res, i, x, arc, le)
+    upper_arc = arc_at_chord(x, arc, 1:le, res.x)
+    lower_arc = arc_at_chord(x, arc, le:length(x), res.x)
+    speed = trailing_edge_speed(res, i, upper_arc, lower_arc, arc[1], arc[end])
+    lower_first, upper_first = abs(res.ue_lower[1, i]), abs(res.ue_upper[1, i])
+    stagnation = lower_arc[1] + lower_first / max(lower_first + upper_first, eps()) *
+                 (upper_arc[1] - lower_arc[1])
+    knots = [arc[end]; reverse(lower_arc); stagnation; upper_arc; arc[1]]
+    values = [-speed; reverse(-abs.(res.ue_lower[:, i])); 0.0;
+              abs.(res.ue_upper[:, i]); speed]
+    order = sortperm(knots)
+    knots, values = knots[order], values[order]
+    keep = [1; [k for k in 2:length(knots) if knots[k] > knots[k - 1] + 1e-9]]
+    return knots[keep], values[keep]
+end
+
+"""
+    neuralfoil_contour_solution(alpha, res, i, x, y, le, arc, cf) -> SectionSolution
 
 Assemble a full-contour [`SectionSolution`](@ref) for case `i` of a NeuralFoil sweep
-`res`: interpolate `res.cp_upper`/`res.cp_lower` (at `res.x`) onto the contour nodes
-`(x, y)` split at the leading edge `le`, carrying the precomputed `cf`.
+`res`: build the one-curve edge velocity ([`velocity_knots`](@ref)), interpolate it
+with a shape-preserving monotone cubic in arc length, and square it into
+`Cp = 1 - ue²` at every contour node. `ue` is the interpolated quantity because it is
+linear in arc length through a stagnation point, where `Cp` is quadratic.
 """
-function neuralfoil_contour_solution(alpha, res, i, x, y, le, cf)
-    up = linear_interpolation(res.x, res.cp_upper[:, i]; extrapolation_bc=Line())
-    lo = linear_interpolation(res.x, res.cp_lower[:, i]; extrapolation_bc=Line())
-    cp = [(k <= le ? up : lo)(clamp(x[k], 0.0, 1.0)) for k in eachindex(x)]
+function neuralfoil_contour_solution(alpha, res, i, x, y, le, arc, cf)
+    knots, values = velocity_knots(res, i, x, arc, le)
+    speed = interpolate(knots, values, FritschButlandMonotonicInterpolation())
+    cp = [1 - speed(clamp(a, first(knots), last(knots)))^2 for a in arc]
     return SectionSolution(alpha, res.cl[i], res.cd[i], res.cm[i],
                            res.confidence[i], x, y, cp, cf)
 end

src/airfoil_aero/neuralfoil.jl

@@ -365,8 +365,10 @@ Full NeuralFoil evaluation returning integrated coefficients and the surface
 pressure distribution reconstructed from the predicted edge-velocity ratios
 (`Cp = 1 - (ue/vinf)^2`) at NeuralFoil's `N` fixed station x/c.
 
-Returns `(; alpha, cl, cd, cm, confidence, x, cp_upper, cp_lower)`, with `x` of
-length `N` and `cp_upper`/`cp_lower` sized `N × n_alpha`.
+Returns `(; alpha, cl, cd, cm, confidence, x, cp_upper, cp_lower, ue_upper,
+ue_lower)`, with `x` of length `N` and the four matrices sized `N × n_alpha`. A
+reconstruction should interpolate `ue` and square afterwards: it is linear in arc
+length through a stagnation point, where `Cp` is quadratic.
 """
 function neuralfoil_section(params::KulfanParameters, alpha, Re;
                             model_size::String="large", weights_dir=nothing,
@@ -384,7 +386,9 @@ function neuralfoil_section(params::KulfanParameters, alpha, Re;
             confidence = Vector{Float64}(sigmoid.(y[1, :])),
             x = compute_optimal_x_points(N),
             cp_upper = Matrix{Float64}(1 .- upper_ue .^ 2),
-            cp_lower = Matrix{Float64}(1 .- lower_ue .^ 2))
+            cp_lower = Matrix{Float64}(1 .- lower_ue .^ 2),
+            ue_upper = Matrix{Float64}(upper_ue),
+            ue_lower = Matrix{Float64}(lower_ue))
 end
 
 """