☔ Raindrops

About

🎯 Solving the wave equation using a finite difference method for implementing the Laplace operator/solver
🧠 Inspired by this example from Recreational Mathematics with Python
🐍 Also available in VPython as raindrop_waves.py, but significantly slower!
👉 Wave equation with velocity-based damping:

$$u_{tt} + \gamma u_t = c^2 \nabla^2 u$$

Where $u$ is the height of water, $u_t$ the velocity, and $\gamma$ the damping coefficient.

Live demo

Structure of the program

DiscreteScalarField
       ↓
LaplaceOperator (FDM stencil)
       ↓
WaveEquationSolver (explicit time stepping)
       ↓
ScalarFieldSurface (visualization)