DIRECTORY / SANDBOXES / FLUID-DYNAMICS.EULER

EULERIAN FLUID DYNAMICS

Navier-Stokes momentum conservation and dye diffusion calculated in typed Float32Array buffers.

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FLUID DYNAMICS HUD

60 FPS

// FLUID DYE PALETTE

VISCOSITY (THICKNESS) WATER

DYE DISSIPATION MEDIUM

[Click & drag across canvas to inject fluid momentum]

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RESEARCH & LEARNING VAULT // Eulerian Fluid Dynamics & Jos Stam Solver

Incompressible Navier-Stokes momentum equations and Stable Fluids semi-Lagrangian advection.

ACADEMIC & ALGORITHMIC REFERENCE

// HISTORICAL ORIGINS

Published by Jos Stam at ACM SIGGRAPH 1999, 'Stable Fluids' revolutionized real-time computer graphics by introducing unconditionally stable semi-Lagrangian advection.

// GOVERNING EQUATIONS

\frac{\partial \mathbf{u}}{\partial t} = -(\mathbf{u} \cdot \nabla)\mathbf{u} + \nu \nabla^2 \mathbf{u} - \frac{1}{\rho}\nabla p + \mathbf{f}, \quad \nabla \cdot \mathbf{u} = 0

// BROWSER IMPLEMENTATION

Solves velocity diffusion, semi-Lagrangian back-tracing advection, and Gauss-Seidel pressure Poisson projection on a 72x72 Eulerian grid.

// GUIDED EXPERIMENTS TO TRY IN THIS SANDBOXNORMAL

1Vortex Karman Street

🎯 Action:Set Viscosity low and drag continuous fast circular strokes in the center.

✨ Observe:Watch turbulent counter-rotating vortex eddies swirl and mix colored dye plumes.

? 🔮 ??? [MYSTERIOUS REGIME]

UNDISCOVERED

🎯 Action:Interact further.

// CURATED PAPERS, RFCS & RESOURCES

Stable Fluidspaper

By Jos Stam (ACM SIGGRAPH 1999)

The landmark paper that made real-time fluid simulation stable at any time step.

Real-Time Fluid Dynamics for Gamesarticle

By Jos Stam (GDC 2003)

Practical implementation guide with C code for grid-based fluid solvers.

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EULERIAN FLUID DYNAMICS

RESEARCH & LEARNING VAULT // Eulerian Fluid Dynamics & Jos Stam Solver