A highly efficient decoupled algorithm for two-phase ferrohydrodynamics model based on Gauge-Uzawa method

Kaiwen Shi, Haohao Li, Haiyan Su and Xiaodi Zhang

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 244, issue C, 1-18

Abstract: In this paper, we design a decoupled, linear and unconditionally energy stable algorithm for the two-phase ferrohydrodynamics (CHFHD) model. The proposed algorithm employs a semi-implicit stabilization approach to solve the phase-field equations, while the ferrohydrodynamics (FHD) part is discretized using the Gauge-Uzawa method. Furthermore, the nonlinear terms of the model are handled by stabilization method with some implicit-explicit treatments. Compared to the standard projection method, our approach resolves the issues related to the initial value selection for pressure p and the handling of artificial boundary conditions on p, which often lead to the formation of boundary layers and reduced numerical accuracy. Finally, several numerical examples are provided to demonstrate the effectiveness and validity of the proposed algorithm.

Keywords: Two-phase FHD; Gauge-Uzawa method; Decoupled; Unconditionally energy stable (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:244:y:2026:i:c:p:1-18

DOI: 10.1016/j.matcom.2025.12.007

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