Home▸Algorithms & AI▸CFL Limit 2D: Space-Time Wave Stability Map

CFL Limit 2D: Space-Time Wave Stability Map

Step a 1D wave equation with an explicit finite-difference scheme and watch the Courant-Friedrichs-Lewy number decide whether it stays stable — a live waveform, a scrubbable space-time waterfall you can drag back through history, and a Courant gauge, all wired to the same grid, wave-speed, timestep and boundary controls.

Algorithms & AI2DAdvanced60 FPS📱 Mobile-adapted⇄ 3D version

Details

CategoryAlgorithms & AI

RenderingCanvas 2D

DifficultyAdvanced

Target FPS60

Controlsgrid resolution and wave speed sliders, fixed/free boundary toggle, adaptive/manual timestep mode toggle, Courant-target or manual-Δt slider, Inject Pulse and Reset Flat buttons, click/drag on the waveform panel to drop a pulse at the pointer, drag on the space-time panel to scrub back through recorded history, Jump to Live button

Canvas 2DNumerical MethodsPerformanceCFL ConditionComputer ScienceSimulation

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The same 1D wave-equation solver as the 3D flagship, redrawn as a layered 2D instrument: a live waveform panel showing the displacement bars, a scrolling space-time waterfall you can drag back through recorded history, and a Courant-number gauge that lights up red the instant r crosses 1. Every control — grid resolution, wave speed, adaptive vs. manual timestep, and now a fixed-vs-free boundary toggle — feeds the same explicit finite-difference scheme and the same CFL stability condition, so you can watch cause (a slider) and effect (stability, or its collapse) in the same frame.

⚙ Under the hood

Step a 1D wave equation with an explicit finite-difference scheme on a layered 2D instrument — a live waveform, a drag-scrubbable space-time waterfall, and a Courant-number gauge — and watch the Courant-Friedrichs-Lewy condition decide whether your timestep is stable as you trade grid resolution, wave speed, boundary condition and timestep size against a fixed computational budget.

Canvas 2DNumerical MethodsPerformanceCFL ConditionComputer ScienceSimulation

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install