The Fluid Dynamics Paint Palette
Eulerian grid Navier-Stokes solver simulating advection, diffusion, and vorticity.
What is The Fluid Dynamics Paint Palette?
Navier-Stokes Computational Fluid Dynamics (CFD) describes how fluid substances—such as water, air, oil, and paint—move, interact, and diffuse under physical forces. Governed by Newton's second law applied to fluid continua, solving these coupled partial differential equations in real time simulates authentic convective advection, viscous diffusion, and swirling turbulent vortex swirls.
How the Interactive Simulation Works
Swirl pigment velocities across a 2D fluid grid to simulate smoke swirls, liquid currents, and turbulent boundary interactions.
Mathematical Formulation & Computational Complexity
The simulation dynamically resolves the state transition function given by:
Incompressible Navier-Stokes grid solvers calculate advection and enforce divergence-free velocity ($\nabla \cdot \mathbf{u} = 0$) via Jacobi pressure Poisson iterations in $\mathcal{O}(I \cdot W \cdot H)$ per time step. Modulating fluid viscosity controls vorticity diffusion and Reynolds number transitions into turbulent eddy currents.
Industrial AI & Real-World Engineering Applications
Simulating wingtip boundary layer separation and turbulent vortex structures in wind tunnel simulations.
Predicting extreme ocean wave surge forces against deep-sea drilling platform support pillars.
Physical pigment diffusion and capillary paper absorption in digital illustration software.