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arXiv · 2306.07112

Adaptive isogeometric phase-field modeling of the Cahn-Hilliard equation: Suitably graded hierarchical refinement and coarsening on multi-patch geometries

Cesare Bracco·Carlotta Giannelli·Alessandro Reali·Michele Torre·Rafael Vázquez
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Abstract

We present an adaptive scheme for isogeometric phase-field modeling, to perform suitably graded hierarchical refinement and coarsening on both single- and multi-patch geometries by considering truncated hierarchical spline constructions which ensures $C^1$ continuity between patches. We apply the proposed algorithms to the Cahn-Hilliard equation, describing the time-evolving phase separation processes of immiscible fluids. We first verify the accuracy of the hierarchical spline scheme by comparing two classical indicators usually considered in phase-field modeling, for then demonstrating the effectiveness of the grading strategy in terms of accuracy per degree of freedom. A selection of numerical examples confirms the performance of the proposed scheme to simulate standard modes of phase separation using adaptive isogeometric analysis with smooth THB-spline constructions.

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Cesare Bracco, Carlotta Giannelli, Alessandro Reali, Michele Torre, Rafael Vázquez. 2023-06-12. Adaptive isogeometric phase-field modeling of the Cahn-Hilliard equation: Suitably graded hierarchical refinement and coarsening on multi-patch geometries. https://arxiv.org/abs/2306.07112

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