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September 2, 2026ESAIM Mathematical Modelling and Numerical AnalysisOpen Access

Error estimates of linear decoupled structure-preserving incremental viscosity splitting methods for the Cahn--Hilliard--Navier--Stokes system

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Authors

BKBaolin KuangHFHongfei FuXLXiaoli Li

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Overview

Numerical analysis demonstrates unconditional optimal error bounds in Cahn-Hilliard-Navier-Stokes models, highlighting efficient structure-preserving fluid simulation.

Key Points

  • To formulate and rigorously analyze linear, decoupled, structure-preserving time discretization schemes for the coupled Cahn–Hilliard–Navier–Stokes two-phase flow model.
  • Integrated incremental viscosity splitting (IVS) with the scalar auxiliary variable (SAV) approach and zero-energy-contribution technique to construct linear, decoupled first- and second-order time-stepping schemes.
  • Conducted multidimensional error analysis using mathematical induction, Stokes regularity estimates, and a user-defined time-dependent parameter.
  • Demonstrated scheme efficiency and verified theoretical convergence rates using numerical simulation benchmarks.
  • Proved the numerical schemes achieve unique solvability, exact mass conservation, and unconditional energy dissipation while solving only constant-coefficient linear equations at each time step.
  • Established an unconditional, optimal convergence rate for the first-order scheme across all primary state variables under multiple spatial norms.
  • Numerical tests confirmed the theoretical accuracy, stability, and computational speed of the proposed structure-preserving framework.

Cite This Study

Kuang et al. (2026) studied this question.

synapsesocial.com/papers/6a97e20ec562ede874ec612chttps://doi.org/10.1051/m2an/2026069
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