THERMA - Heat Equation Visualizer

An interactive browser-based visualizer for the heat equation in 1D and 2D, using finite differences (explicit Euler method).

Live demo: https://heat-eq.vercel.app

Overview

THERMA solves the heat equation:

• 1D: $\frac{\partial u}{\partial t} = \alpha \frac{\partial^2 u}{\partial x^2}$
• 2D: $\frac{\partial u}{\partial t} = \alpha \nabla^2 u$

using an explicit finite difference scheme with automatic stability control (CFL condition).

1D Mode (default)

• Interactive drawing: Click and drag on the plot to draw custom initial temperature profiles
• 8 presets: Sine wave, Gaussian, step function, triangle, two humps, random, square wave, sawtooth
• Adjustable parameters: Thermal diffusivity, spatial resolution, segment length, simulation speed, brush size
• Boundary conditions: Dirichlet (fixed temperature) and Neumann (insulated/zero flux)
• Real-time visualization: Color-coded temperature profile with space-time heatmap

2D Mode

• Heat brush: Click and drag on the 2D surface to paint heat. Hold to accumulate. Right-click to cool.
• 6 presets: Center hotspot, four corners, ring, cross, random spots, diagonal
• Adjustable parameters: Thermal diffusivity, grid resolution (N x N), domain size, brush radius, brush temperature, simulation speed
• Boundary conditions: Dirichlet (fixed temperature at edges) and Neumann (insulated/zero flux)
• Real-time heatmap: Color-coded 2D temperature field with bilinear interpolation

Usage

1. Open index.html (1D) or index2d.html (2D) in a web browser
2. In 1D: draw an initial condition or select a preset; in 2D: paint heat with the brush
3. Adjust physics parameters (diffusivity, resolution, domain size)
4. Set boundary conditions (Dirichlet or Neumann)
5. Click Play to run the simulation, or Step to advance manually
6. Use the toggle button in the header to switch between 1D and 2D modes

Files

File	Description
index.html	1D Heat Equation Visualizer (default)
index2d.html	2D Heat Equation Visualizer

No dependencies, no build step -- just open in a browser.

Author

Bhaskar Krishnamachari, University of Southern California (USC)

License

This project is licensed under the PolyForm Noncommercial License 1.0.0.