Pocket Black Hole vs ViscousJoukowski

Pocket Black Hole is a simple app that allows you to play with the light-bending effect of a black hole. Take a selfie, or a photo of your friends, with a black hole! A black hole is a very compact and massive object, in fact its gravity is so strong that it will bend the path of light passing close by. If the light gets too close, it cannot escape, and that is why the object appears to us as a black hole in the sky. Our app does not use the full equations from Einstein's theory of general relativity to compute this distortion. Instead we are using a much simpler formula to create a similar visual effect.

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.