pm (Parameswaran-Mandal)

← Components

intsharp/sharpening.py

Parameswaran-Mandal sharpening

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

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

\[ \text{RHS} = -K \alpha(1-\alpha)(1-2\alpha) + \epsilon (1-2\alpha) |\nabla\alpha| \]

where \( K = 1/(4\epsilon^2) \).

pm_cal (calibrated PM)

Same structure, but the cubic term uses a fixed calibrated constant \( C_{\mathrm{PM}} \) instead of \( K(\varepsilon)=1/(4\varepsilon^2) \). CAL refers to this coefficient being set from a validated calibration (see code constant C_PM_CALIBRATED in sharpening.py). Use sharpening_method: pm_cal in YAML.

Update:

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

Parameters:

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

Source

A stable interface-preserving reinitialization equation for conservative level set method (PDF)

BibTeX:

@article{parameswaran_mandal_stable,
  author  = {Parameswaran, S. and Mandal, J. C.},
  title   = {A stable interface-preserving reinitialization equation for conservative level set method},
  journal = {},
  year    = {},
  note    = {See PDF for full citation. Related: arXiv:2012.08747.}
}