The 3D version renders the wing pair and reads off a closed-form estimate of the fling circulation (Γ ≈ πc²·dθ/dt, attenuated by an ad-hoc exponential factor for the clap gap). This 2D companion instead solves for the circulation every frame with a proper discrete-vortex method (DVM) — the same family of technique used in the flapping-flight CFD literature (e.g. Wang 2000; Ansari, Phillips & Stanford 2006).
Each wing is a flat plate viewed edge-on (a spanwise cross-section). One bound point-vortex sits at its quarter-chord; a control point at three-quarter-chord enforces the classical thin-airfoil no-penetration condition. Solving the resulting 2×2 linear system for both wings simultaneously — not independently — is what captures the real "wall effect" of the clap: each wing's presence changes the flow the other wing sees, which is the actual mechanism Weis-Fogh and Lighthill described, rather than a fudge factor bolted on afterward.
Biot-Savart (2D point vortex, desingularized):
v(p) = Γ/(2π) · (-dy, dx) / max(r², r_core²), d = p - r_vortex
No-penetration at each wing's 3/4-chord control point C_i:
Σ_j induced(Γ_j, C_i)·n_i = v_body(C_i)·n_i
Kelvin's circulation theorem (every step):
ΔΓ_wake,i = -(Γ_i(t) - Γ_i(t-dt)) -- shed at the trailing edge
Reynolds number: Re = U c / ν (νair ≈ 1.5×10⁻⁵ m²/s)
Shed wake vortices then convect under their own mutual Biot-Savart induction plus the bound vortices — real N-body vortex dynamics, not decorative particles. The live bound Γ readout is whatever that linear system actually returns each frame; the fling lift boost divides it by a separately-solved isolated-wing reference (same control-point equation with the partner wing's influence and the wake switched off), so the ratio reflects genuine mutual-induction gain rather than a preset curve.
One consequence of solving this honestly: in the idealized inviscid limit, two flat plates in full contact (zero gap) make the linear system singular — the circulation should formally diverge, which is exactly the "trapped air accelerates arbitrarily fast" idealization Lighthill (1973) described. This sim floors the clap gap and clamps the solve to stay numerically stable while still showing the genuine sharp rise as the gap narrows, rather than silently copying the 3D version's smoothing.