Navier-Stokes 2D Simulation💧

Welcome to Navier-Stokes 2D Simulation, where we flex our brain cells and GPUs to simulate Navier-Stokes equations.

Powered by Rust 🦀 and Bevy 🚀, this project is your gateway to fluid dynamics with vibes.

📚 Conditions

• Steady flow.
• Incompressible flow.
• No gravity effects.
• Pressure gradient is exists.
• Boundary conditions are y=[0, b].
• u(y) = U at y=0; u(y) = 0 at y=b.
• Using metric units.

📝 Flow Profile

$$ u(y) = \frac{1}{2\mu} \nabla p \left(b^2 - by\right) + U \left(1 - \frac{y}{b}\right) $$

🚀 WASM Demo

https://rayato159.github.io/navier-stokes-simulation/

📝 Presentation

PDF Slide

🎯 What's the Vibe?

We're talking 2D fluid sims that are smoother than your morning coffee pour.

• Solves Navier-Stokes equations (yes, the math that makes fluids flow 🧠💦).
• Uses Rust for max performance and Bevy for stunning visuals.

🛠️ Setup: Get Yo' Fluids Flowing

1. Clone the Repo 🖥️

   git clone https://github.com/Rayato159/navier-stokes-simulation.git
   cd navier-stokes-simulation

2. Run the Simulation 🚀

   cargo run

3. Key Controls 🎮

   Space: Play/Pause the simulation.
   

💡 Features

• Real-time 2D fluid simulation: Smooth and satisfying, like butter on pancakes.
• Customizable parameters: Adjust dynamics viscosity, pressure rate, and more.
• Bevy-powered rendering: Leverages the ECS magic for clean visuals and top-tier performance.

📑 References

• https://www.grc.nasa.gov/www/k-12/airplane/nseqs.html
• https://www.simscale.com/docs/simwiki/numerics-background/what-are-the-navier-stokes-equations/