A sharp-diffuse interface model for intermittent and isolated topological transitions

Raaghav Ramani

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arXiv · 2608.24030

A sharp-diffuse interface model for intermittent and isolated topological transitions

Raaghav Ramani

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Abstract

We propose a hybrid sharp-diffuse interface representation for modeling intermittent and isolated topological transitions during Cahn-Hilliard phase coarsening. Away from topological events, the evolution is approximated by the Mullins-Sekerka sharp-interface limit system and computed using a boundary integral formulation. When diffuse transition layers overlap, a novel interface surgery algorithm resolves topology changes through a localized Cahn-Hilliard pseudo-time evolution, after which the sharp-interface calculation is resumed. We develop the mathematical formulation underlying this decomposition, present a simple two-dimensional numerical implementation, and simulate a mass-exchange problem with interface coalescence. By localizing the diffuse evolution to topological events, the method achieves a speedup of two to three orders of magnitude over conventional diffuse-interface simulations.

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physics.comp-ph cs.NA math.NA physics.flu-dyn

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Raaghav Ramani. 2026-08-25. A sharp-diffuse interface model for intermittent and isolated topological transitions. https://arxiv.org/abs/2608.24030

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