Fluidrix - 2D Fluid Dynamics Simulator

A lightweight Ruby implementation of 2D fluid dynamics based on the Navier-Stokes equations using Jos Stam's stable fluid method.

Installation

gem install fluidrix

Or add to your Gemfile:

gem 'fluidrix'

Math Overview

The simulator solves the incompressible Navier-Stokes equations:

Continuity Equation

$$\nabla \cdot \mathbf{u} = 0$$

Momentum Equation

$$\frac{\partial \mathbf{u}}{\partial t} + (\mathbf{u} \cdot \nabla)\mathbf{u} = -\frac{1}{\rho}\nabla p + \nu \nabla^2 \mathbf{u} + \mathbf{f}$$

Where:

• $\mathbf{u} = (u, v)$ - velocity field
• $p$ - pressure
• $\rho$ - density
• $\nu$ - kinematic viscosity
• $\mathbf{f}$ - external forces

Algorithm Steps (Per Time Step)

1. Add Forces - Apply external forces to velocity field
2. Diffuse - Viscosity spreads velocity (Gauss-Seidel iteration)
3. Project - Enforce mass conservation (pressure solve)
4. Advect - Move velocity along itself
5. Project - Final pressure correction

Usage

require 'fluidrix'

# Create simulator (width, height, viscosity, dt)
sim = Fluidrix::Simulator.new(100, 100, 0.0001, 0.1)

# Add velocity (x, y, amount)
sim.add_velocity(50, 50, 10.0, 5.0)

# Add density/dye (x, y, amount)
sim.add_density(50, 50, 1.0)

# Step simulation forward
sim.step

# Get field data
velocity_field = sim.velocity
density_field = sim.density

Output Formats

The simulator provides raw arrays for:

• Velocity: velocity[x][y] = {u: float, v: float}
• Density: density[x][y] = float

Example Visualization

require 'fluidrix'

sim = Fluidrix::Simulator.new(128, 128)

# Add circular impulse
64.times do |i|
  angle = i * Math::PI * 2 / 64
  sim.add_velocity(64 + Math.cos(angle) * 10, 
                   64 + Math.sin(angle) * 10,
                   Math.cos(angle) * 5,
                   Math.sin(angle) * 5)
end

100.times { sim.step }

Interactive Visualization

Open visualize.html in a browser for an interactive fluid simulation:

• Click and drag to add fluid and velocity
• Adjust viscosity, diffusion, and resolution
• Real-time velocity field visualization

Parameters

Parameter	Description	Typical Range
width, height	Grid resolution	32-512
viscosity	Fluid thickness	0.00001 - 0.1
dt	Time step	0.01 - 0.5

License

MIT License - feel free to use in your projects!