Check POLAR_MATRICES forwarddiff on affine tables instead of NeuralFoil's

The ram-air wing's tip sections are ~70%-thick slices (#361) on which
NeuralFoil returns Cd=1 at every alpha, and those outputs differ with the
runner's CPU, so the LOOP solve lands on one of two different solutions
depending on the runner. Tables that are affine in (alpha, delta) make the
bilinear interpolation exact, keep every panel attached, and are the same
bits on every machine.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

Author: 1-Bort-1

test/solver/test_forwarddiff.jl

@@ -5,6 +5,25 @@ using Test
 
 relative_error(jac, reference) = maximum(abs.(jac .- reference)) / maximum(abs, reference)
 
+# Four-section arc whose POLAR_MATRICES tables are affine in (alpha, delta), so the
+# bilinear interpolation is exact and has no kinks at the grid knots.
+function affine_matrix_wing(n_panels)
+    alphas = deg2rad.(-5:5:25)
+    deltas = deg2rad.(-3:3:3)
+    cl = [0.2 + 5.5alpha + 1.5delta for alpha in alphas, delta in deltas]
+    cd = [0.03 + 0.2alpha + 0.05delta for alpha in alphas, delta in deltas]
+    cm = [-0.05 - 0.1alpha - 0.3delta for alpha in alphas, delta in deltas]
+    wing = Wing(n_panels, spanwise_distribution=LINEAR)
+    radius = 3.0
+    for phi in deg2rad.((50, 17, -17, -50))
+        le = [0.0, radius * sin(phi), radius * (cos(phi) - 1)]
+        add_section!(wing, le, le .+ [1.0, 0.0, 0.0], POLAR_MATRICES,
+            (alphas, deltas, cl, cd, cm))
+    end
+    refine!(wing)
+    return wing
+end
+
 @testset "ForwardDiff linearize" begin
     n_panels = 10
     span = 20.0
@@ -57,20 +76,9 @@ relative_error(jac, reference) = maximum(abs.(jac .- reference)) / maximum(abs,
     end
 
     @testset "AutoForwardDiff matches AutoFiniteDiff (LOOP, POLAR_MATRICES)" begin
-        # At this operating point the LOOP solve converges the mid-span
-        # panels' local alpha to ~6.5-9.1deg and the tip panels' to
-        # ~14.9-15.0deg. The default 5deg-spaced alpha_range=-5:5:15 puts the
-        # tip cluster within ulp-scale distance of the 15deg knot on some
-        # platforms (Windows, Julia 1.12), so AutoForwardDiff and the FD
-        # reference land on opposite sides of that non-differentiable kink
-        # and disagree by several percent (#360). Offset the grid so no knot
-        # is near either cluster (margin >0.8deg here vs <0.04deg before).
-        ram_wing = ram_air_matrix_wing(; n_panels=8, n_sections=4,
-            alpha_range=deg2rad.(-2:5:23),
-            delta_range=deg2rad.(-3:3:3),
-        )
-        ram_body = BodyAerodynamics([ram_wing])
-        ram_solver = Solver(ram_wing.n_panels, ram_wing.n_unrefined_sections;
+        matrix_wing = affine_matrix_wing(8)
+        matrix_body = BodyAerodynamics([matrix_wing])
+        matrix_solver = Solver(matrix_wing.n_panels, matrix_wing.n_unrefined_sections;
             aerodynamic_model_type=VSM,
             rtol=1e-11,
             solver_type=LOOP,
@@ -84,13 +92,13 @@ relative_error(jac, reference) = maximum(abs.(jac .- reference)) / maximum(abs,
                 zeros(3)]
 
         jac_fwd, _, conv_fwd = VortexStepMethod.linearize(
-            ram_solver, ram_body, y_op;
+            matrix_solver, matrix_body, y_op;
             theta_idxs=1:4, va_vec_idxs=5:7, omega_idxs=8:10,
             aero_coeffs=true, backend=AutoForwardDiff())
         @test conv_fwd
 
         jac_fd, _, conv_fd = VortexStepMethod.linearize(
-            ram_solver, ram_body, y_op;
+            matrix_solver, matrix_body, y_op;
             theta_idxs=1:4, va_vec_idxs=5:7, omega_idxs=8:10,
             aero_coeffs=true, backend=nothing)
         @test conv_fd