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2D Navier–Stokes Fluid Simulation

Interactive Real-Time Viscous Fluids

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Incompressible Navier–Stokes Equations

\[ \begin{gather} \rho\left(\frac{\partial \mathbf{u}}{\partial t} + (\mathbf{u} \cdot \nabla)\mathbf{u}\right) = \mu \nabla^2 \mathbf{u} -\nabla p + \mathbf{f} \\ \\ \nabla \cdot \mathbf{u} = 0 \end{gather} \]

TIP: Left-drag adds velocity + dye — hold Shift to add dye only.
Right-click & drag (or two-finger drag on touch) pushes fluid with velocity only.