🌊 Fluid Dynamics Simulation

A real-time, interactive 2D fluid simulation that visualizes complex fluid dynamics using the Navier-Stokes equations. This physics-based simulation demonstrates computational fluid dynamics principles with an intuitive, visually engaging interface.

Fluid Density Visualization

Velocity Vector Field Visualization

✨ Features

• Interactive Fluid Dynamics: Click and drag to introduce forces and dye into the simulation
• Real-time Physics: Accurate numerical approximation of the Navier-Stokes equations
• Dual Visualization Modes: View both the fluid density and underlying velocity field
• Customizable Parameters: Adjust diffusion, viscosity, and other physical properties
• Optimized Performance: Efficiently implemented algorithms for smooth real-time interaction

🧪 Mathematical Foundation

The simulation solves the incompressible Navier-Stokes equations:

Where:

• u: Velocity field
• p: Pressure
• ρ: Density
• ν: Viscosity coefficient
• f: External forces

With the incompressibility constraint:

Navier-Stokes Equations

The simulation solves the incompressible Navier-Stokes equations:

∂u/∂t + (u ⋅ ∇)u = -(1/ρ)∇p + ν∇²u + f

Where:

• u: Velocity field
• p: Pressure
• ρ: Density
• ν: Viscosity coefficient
• f: External forces

With the incompressibility constraint:

∇ ⋅ u = 0

Prerequisites

# Install required dependencies
pip install numpy pygame

Running the Simulation

# Launch the simulation
python fluidsim.py

🎮 Controls

Key/Action	Description
Mouse Drag	Add fluid density and velocity
Space	Pause/Resume simulation
V	Toggle velocity visualization
C	Clear the simulation
R	Add random forces
+/-	Increase/decrease simulation speed
ESC	Exit application

🏗️ Code Architecture

fluid-simulation/
├── fluidsim.py         # Main application entry point
├── fluid_simulator.py  # Core fluid dynamics solver
├── visualization.py    # Rendering and visualization components
├── utils/
│   ├── vector_field.py # Vector field operations
│   └── math_utils.py   # Math helper functions
└── tests/              # Test suite

Key Classes

• FluidSimulator: Core physics engine implementing Navier-Stokes solver
• FluidRenderer: Handles visualization of density and velocity fields
• SimulationController: Manages user input and simulation parameters

💡 Implementation Details

The implementation follows Jos Stam's "Real-Time Fluid Dynamics for Games" approach with several optimizations:

1. Velocity Field Update:

   • Advection → Diffusion → External Forces → Projection

2. Density Field Update:

   • Advection → Diffusion → Source Addition

3. Projection Method:

   • Computes pressure to ensure mass conservation
   • Uses multi-grid or conjugate gradient methods for efficiency

🔧 Customization

The simulation offers various parameters for experimentation:

# Example configuration
config = {
    'grid_size': 128,
    'diffusion_rate': 0.0001,
    'viscosity': 0.00001,
    'dt': 0.1,
    'iterations': 20
}

🔮 Future Enhancements

• GPU acceleration using OpenCL/CUDA
• 3D fluid simulation
• Interaction with rigid bodies
• Advanced rendering with particle systems
• Web-based version using WebGL

📚 Resources

• Real-Time Fluid Dynamics for Games by Jos Stam
• Fluid Simulation for Computer Graphics by Robert Bridson
• Physically Based Modeling: Principles and Practice by Andrew Witkin and David Baraff

📄 License

This project is licensed under the MIT License - see the LICENSE file for details.

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