lcls_2012 (Localized CLS, 2012)

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intsharp/sharpening.py

Localized CLS (2012)

Supports: 1D and 2D (selected automatically based on domain)

RHS for the volume fraction \( \alpha \):

\[ \text{RHS} = \beta \epsilon \nabla^2\alpha - \beta \nabla\cdot\bigl(\alpha(1-\alpha)\mathbf{n}\bigr) \]

Localization: \( \beta = 4\alpha(1-\alpha) \), which peaks at the interface and vanishes in the bulk. Unit normal \( \mathbf{n} = \nabla\alpha/|\nabla\alpha| \).

Update:

\[ \alpha^{n+1} = \alpha^n + \Delta t \cdot \Gamma \cdot \text{RHS} \]

Parameters:

  • eps_target: Target interface thickness \( \epsilon \)
  • strength: Sharpening strength \( \Gamma \)