ViscousJoukowski vs Particle Life

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.

What can simple rules create? Particle Life is a free science laboratory for iPhone and iPad. Change how colorful particles attract and repel one another, then watch clusters and moving patterns emerge. LEARN BY EXPERIMENTING Seven guided experiments invite you to predict, change one variable, observe and explain. Explore attraction, unequal interactions, distance, friction, boundaries, emergence and reactions. Keep predictions and observations alongside your saved worlds. TRY REACTIONS Build bonded structures and add acid particles. When two acids attach to the same structure, its bonds break into loose fragments and the reacting acids become harmless spent particles. Change the number of acids needed, attachment strength and recovery time. Explore this optional toy-chemistry laboratory in 2D and 3D, or follow the new guided experiment, Two acids, one structure. MAKE THE RULES Edit how each species responds to every other species. Adjust attraction, repulsion, interaction distances, particle count, friction and world boundaries. Use exact values, original presets or randomized rules to follow your curiosity. EXPLORE IN 2D AND 3D Add, erase, attract and repel particles with touch tools. Pan, zoom and orbit. Pause, advance one step, inspect a particle or replay a compatible starting arrangement while keeping your edited rules. SAVE YOUR DISCOVERIES Save complete worlds with notes, export and import .particlelife files, and share a still picture through the iOS share sheet. A COMPLETE FREE LABORATORY Every tool and experiment is free. Optional one-time tips support development without unlocking content. No accounts, ads or subscriptions. Simulations and notes stay on your device unless you choose to share them. These are simplified artificial-life and invented toy-chemistry rules, not validated biological or real acid-chemistry models. The particles are not living organisms. Larger populations and demanding settings can slow the simulation. Designed for iPhone and iPad, with portrait and landscape layouts.