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2 days ago
- **Momentum Equation**: \[ \frac{\partial \mathbf{u}}{\partial t} + (\mathbf{u} \cdot \nabla) \mathbf{u} = -\frac{1}{\rho} \nabla p + \...
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Boltning XL v1 Lightning
Creation Summary by Vincent
Navier-Stokes Momentum Equation Visualization
This image visualizes the Navier-Stokes momentum equation, illustrating fluid dynamics with velocity, pressure, and viscosity effects. It shows complex flow patterns driven by external forces and incompressibility.
Created by Boris Krumov on Dec 11, 2025 using the Boltning XL v1 Lightning AI image generator model.
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Creation Settings
- Text Prompts
- - **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 ...Weight: 1.8- **Recursive Solution**: Apply a multi-pass scheme (e.g., semi-implicit Euler) with \(k\) levels of recursion: \[ \mathbf{u}^{n+1} = \mathbf{u}^n + \Delta t \left[ -\frac{1}{\rho} \nabla p^{n+1} + \nu \nabla^2 \mathbf{u}^n + \mathbf{f}^n - (\mathbf{u}^n \cdot \nabla) \mathbf{u}^n \right] \] ...Weight: 0.2- **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}) ...Weight: -0.4
- Model
- Initial Resolution
Medium
- Aspect Ratio
1:1
- Runtime
Long
- Overall Prompt Weight
100%
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