🌀 2D Fluid Demo

A real-time 2D fluid simulation written in Unity using fragment shaders (Blit-based), inspired by PavelDoGreat/WebGL-Fluid-Simulation.

This project implements a simplified yet physically-grounded fluid solver in screen space, supporting dye injection, velocity advection, incompressibility enforcement, and vorticity confinement.

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🚀 Features

• 💧 Real-time 2D fluid dynamics (Eulerian grid-based)
• 🎨 Mouse-driven dye and velocity injection (splatting)
• 🌀 Vorticity confinement to enhance visual swirls
• 💨 Velocity and dye advection via semi-Lagrangian scheme
• 🧮 Incompressibility enforcement via iterative pressure solve
• 🎞️ Dissipation control for dye and velocity fading
• 🧪 Fully GPU-based, implemented in fragment shaders

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📐 Physical Principles

This demo follows standard grid-based fluid simulation principles outlined in Jos Stam's "Stable Fluids" model:

1. Advection

Transports quantities (velocity, dye) along the velocity field:

$$ q(\mathbf{x}, t + \Delta t) = q(\mathbf{x} - \mathbf{v} \Delta t, t) \cdot \text{dissipation} $$

2. Incompressibility

Enforces zero divergence of the velocity field via pressure projection:

$$ \nabla \cdot \mathbf{v} = 0 \quad \Rightarrow \quad \mathbf{v} \gets \mathbf{v} - \nabla p $$

3. Pressure Solve

Solves the Poisson equation iteratively:

$$ \nabla^2 p = \nabla \cdot \mathbf{v} $$

4. Vorticity Confinement

Reintroduces fine swirling motion lost due to dissipation:

$$ \mathbf{f}_\omega = \epsilon (\nabla |\omega| \times \hat{\omega}) $$

Where ω is the scalar curl, and ε is the curl strength parameter.

5. Splatting (Impulse Injection)

Injects velocity and dye based on mouse position and drag delta using Gaussian falloff.

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🧱 Shader Modules

Shader	Purpose
Advection.shader	Advect velocity or dye based on velocity field
Divergence.shader	Compute divergence of velocity
Pressure.shader	Solve pressure iteratively
GradientSubtract.shader	Project velocity to incompressible field
SplatDye.shader	Inject dye at mouse position
SplatVelocity.shader	Inject velocity impulse
Vorticity.shader	Compute curl of velocity
VorticityForce.shader	Add swirl force to velocity
Display.shader	Render final dye texture

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🕹️ Controls

• Left Click + Drag: Injects dye and velocity (directional)
• Hold: Continuous injection
• Adjust parameters in FluidSim.cs for tuning radius, viscosity, etc.

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🛠️ Dependencies

• Unity 6

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📁 Project Structure

Assets/
├── Shaders/              # All simulation shaders
├── Scripts/
│   └── FluidSim.cs       # Main simulation logic

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🎛️ Parameters & Tips

你可以在 Unity Inspector 中实时调整以下参数以控制模拟行为：

🧪 Simulation Settings

Parameter	Description
simResolution	Resolution of the simulation grid (higher = more detail, more expensive)
pressureIterations	Number of Gauss-Seidel iterations for pressure solve (incompressibility)
deltaTimeMin/Max	Clamped delta time per frame, helps ensure numerical stability
velocityMultiplier	Scales the strength of injected velocity from mouse drag
viscosity	Controls how quickly the velocity field dissipates over time
decay	Controls how quickly dye fades over time (0 = never fade)

🎨 Splat Settings

Parameter	Description
splatRadius	Radius of mouse splat for both dye and velocity injection (in UV units)
splatDyeColor	Color of injected dye (can be customized to simulate different materials)

🌀 Vorticity Settings

Parameter	Description
curlStrength	Controls how strongly vorticity force reintroduces swirling motions

💡 Tip: If you feel the dye stays static, try increasing velocityMultiplier, curlStrength or reducing viscosity.

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📖 References

• Stable Fluids by Jos Stam (1999)
• WebGL Fluid Simulation by PavelDoGreat
• Bridson, R. (2015). Fluid Simulation for Computer Graphics

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🧠 TODO

• Add GUI sliders for parameters
• Optimize with compute shaders
• Add obstacles / boundary conditions
• GPU-based multi-resolution support

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📸 Preview

Swirling flow induced by directional dye injection with vorticity confinement

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📜 License

MIT License – free to use, modify and share.