Eulerian Fluid Dynamics

Navier-Stokes Grid Solver

Theory & Scientific Principles

Navier-Stokes Equations: Governs viscous, incompressible fluid flow through momentum and continuity:

∂u/∂t = -(u·∇)u + ν∇²u - (1/ρ)∇p + f
∇ · u = 0 (Incompressibility)

1. Semi-Lagrangian Advection: Particles back-trace velocities through space to stably transport dye and momentum.

2. Jacobi Pressure Poisson Solver: Enforces zero divergence by iteratively computing pressure fields p via ∇²p = ∇·u.

3. Vorticity Confinement: Amplifies turbulent eddies and micro-vortices otherwise damped by numerical dissipation.

Controls: Drag cursor to inject dye & velocity. Adjust viscosity, vorticity, and decay in real time.

Viscosity ν (Pa·s)

Vorticity Confinement ε (coeff)

Dye Diffusion κ (m²/s)

Dye Dissipation Rate (%/frame)

Brush Inject Radius (cells)

Time Step Δt (seconds)

Grid Resolution: 100 × 100 cells

Reynolds No. (Re): 8,420

Max Velocity (|u|): 0.00 m/s

Kinetic Energy: 0.00 J

Simulation FPS: 60.0

Eulerian Navier-Stokes Grid