ViscousJoukowski vs Aerobench

Are you interested in fluid dynamics? Viscous Joukowski simulates the flow around a Joukowski airfoil by solving the two-dimensional incompressible Navier–Stokes equations directly on your device. For teachers, students, and curious aerodynamicists, it provides an interactive way to explore how viscosity changes lift, drag, pressure, boundary layers, separation, and wake formation. Watch vorticity, speed, pressure, and streamlines evolve around the airfoil. Change the angle of attack, thickness, and camber by dragging directly on the flow field, or use precision controls. Adjust the Reynolds number to explore steady flow, separated wakes, starting vortices, and vortex shedding. Surface-pressure curves and aerodynamic-force estimates update as the simulation develops. The app also includes the classical analytical Joukowski potential-flow solution. Overlay it on the computed viscous pressure distribution to see where the ideal textbook model agrees with—or departs from—the Navier–Stokes result. In the potential solution, circulation is selected using the Kutta condition; in the viscous simulation, circulation and the wake develop dynamically from the no-slip flow. All calculations run locally using Apple MLX and GPU-accelerated Fourier methods. No server, account, or cloud computation is required.

Aerobench is a digital wind tunnel. Set the airspeed and the angle of attack of a wing section, watch the air flow around it in real time, then measure what you see. Nothing is pre-recorded: every frame comes out of a fluid solver running on your device's graphics processor. Separation, wake, vortices and stall are not drawn, they emerge from the computation. SEE THE FLOW • Thousands of streaks follow the computed velocity field. Coloured by speed (blue slow, white fast) or by vorticity (blue laminar, orange vortical), they make the border between attached and separated flow visible. • Surface pressure is painted straight onto the wing, from the blue of suction to the orange of overpressure. • Free 3D view: rotate the wing with your finger, zoom, return to a side view. MEASURE • Lift coefficient, drag coefficient, lift-to-drag ratio and lift per metre of span, updated continuously. • Separation point: the app detects flow reversal at the wall and tells you where the boundary layer leaves the surface, as a fraction of chord. • Pressure coefficient curve along the section, compared with the inviscid reference solution. • Automatic polars: sweep the angle of attack, let the tunnel settle and average each angle, and get the lift and drag curves. CSV export. THE MODELS, IN PLAIN WORDS The app always states which model produced which number. • Viscous solver, lattice Boltzmann method (D2Q9). The fluid is described by populations of particles that, at each time step, collide locally and then stream to neighbouring cells. In the low Mach number limit this scheme solves the incompressible Navier-Stokes equations. Scales too fine for the grid are modelled by a Smagorinsky subgrid term. The wing is a no-slip wall treated by bounce-back; forces come from momentum exchange at the wall, not from an empirical formula. • Inviscid reference, Hess-Smith panel method with a Kutta condition at the trailing edge. It gives the lift and the pressure of a perfect potential flow. Shown dashed next to the viscous measurement, it reveals what viscosity and separation take away from the ideal theory. SCIENTIFIC HONESTY A phone cannot resolve the millions of Reynolds of real flight. The app shows side by side the real Reynolds number of your conditions and the one actually simulated. At that scale the boundary layer stays laminar and separates earlier than in flight: the stall angle is pessimistic and drag overestimated. The trends stay right and comparable from one airfoil to the next. Absolute values do not replace a wind tunnel test. The computation is two-dimensional: no wingtip effects, no induced drag, no shock waves. CREATE YOUR OWN AIRFOILS • Parametric drawing: camber, camber position, thickness and trailing-edge reflex, with instant preview and checking. • Free sketching: drag control points, the curve is interpolated and validated continuously. • Four-digit NACA generation. • Import of coordinates in Selig and Lednicer formats. Every airfoil you create is tested exactly like the built-in ones, then renamed, duplicated or exported. BUILT-IN AIRFOILS NACA 0012, 2412 and 4412, plus the NASA SC(2)-0412 and SC(2)-0712 supercritical sections, from published coordinates. WHO IT IS FOR Students of physics, fluid mechanics or aeronautics. Student pilots who want to see what stall actually means. Modellers and designers comparing sections. Teachers looking for a demonstration they can manipulate. PRIVACY Everything is computed on device. No account, no sign-in, no data collection. The app works entirely offline.