ViscousJoukowski vs Navier Stokes Explained

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.

The Navier-Stokes equations describe how every liquid and gas moves. They are usually met as a wall of symbols. Here they are a tank of water you can hold. A real three-dimensional fluid solver runs on your iPhone's GPU. Drop a column of water, stir a tank, push a flow past a sphere, or turn on Tilt and let gravity follow your phone. Then look inside: color the water by speed, pressure or rotation, tap anywhere to measure it, and open the live values to see each term of the equation as an arrow at that point. In still water the pressure arrow and the gravity arrow cancel, which is what the equation says they must do. FOUR GUIDED LESSONS Predict, watch, compare, explain. • Why does a swirl fade? The same stir in two liquids, 10,000 times apart in viscosity. • What holds water up? Measure pressure at two depths. • How does flow turn? A pulse of water meets a solid sphere. • Why doesn't water squash? The same falling column with pressure switched off. A LAB, NOT A VIDEO • Gravity, viscosity and stirring strength are yours to change, with a live Reynolds number. • Velocity and pressure arrows, tracer trails, pause, single-step and half speed. • Every term of the equation opens a plain-language explanation and an experiment to try. • Works offline. No account.