ArticleJournal of nonlinear science2022
An Explicit Adaptive Finite Difference Method for the Cahn-Hilliard Equation.
Article in Journal of nonlinear science, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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2 citing papers in PubMed.
- Mechanistic model of phase-transitioning therapeutics injected into poroelastic tissue for improved targeting of superficial tumors.Scientific reports · 2026Article
- Mechanistic model of phase-transitioning therapeutics injected into poroelastic tissue for improved targeting of superficial tumors.Research square · 2025Article
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7 authors.
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Abstract
In this study, we propose an explicit adaptive finite difference method (FDM) for the Cahn-Hilliard (CH) equation which describes the process of phase separation. The CH equation has been successfully utilized to model and simulate diverse field applications such as complex interfacial fluid flows and materials science. To numerically solve the CH equation fast and efficiently, we use the FDM and time-adaptive narrow-band domain. For the adaptive grid, we define a narrow-band domain including the interfacial transition layer of the phase field based on an undivided finite difference and solve the numerical scheme on the narrow-band domain. The proposed numerical scheme is based on an alternating direction explicit (ADE) method. To make the scheme conservative, we apply a mass correction algorithm after each temporal iteration step. To demonstrate the superior performance of the proposed adaptive FDM for the CH equation, we present two- and three-dimensional numerical experiments and compare them with those of other previous methods.
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