- **Momentum Equation**: \[ \frac{\partial \mathbf{u}}{\partial t} + (\mathbf{u} \cdot \nabla) \mathbf{u} = -\frac{1}{\rho} \nabla p + \...

- **Momentum Equation**: \[ \frac{\partial \mathbf{u}}{\partial t} + (\mathbf{u} \cdot \nabla) \mathbf{u} = -\frac{1}{\rho} \nabla p + \nu \nabla^2 \mathbf{u} + \mathbf{f}(\mathbf{x}, t) \] - \(\mathbf{u}(\mathbf{x}, t)\): Velocity vector field (\(\mathbf{u} = [u_x, u_y, u_z]\)), dictating color ...

- **Recursive Solution**: Apply a multi-pass scheme (e.g., semi-implicit Euler) with \(k\) levels of recursion: \[ \mathbf{u}^{n+1} = \mathbf{u}^n + \Delta t \left[ -\frac{1}{\rho} \nabla p^{n+1} + \nu \nabla^2 \mathbf{u}^n + \mathbf{f}^n - (\mathbf{u}^n \cdot \nabla) \mathbf{u}^n \right] \] ...

- **Glow & Outline**: Use Laplacian-of-Gaussian (LoG) for edge enhancement: \[ \nabla^2 G(\mathbf{x}, \sigma) * I(\mathbf{x}) = \left[ \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} \right] \left( \frac{1}{2\pi \sigma^2} e^{-\frac{|\mathbf{x}|^2}{2\sigma^2}} \right) * I(\mathbf{x}) ...