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Stability and Error Analysis of SAV Semi-Discrete Scheme for Cahn-Hilliard-Navier-Stokes Model
Haijun Gao, Xi Li and Minfu Feng

Numer. Math. Theor. Meth. Appl. DOI: 10.4208/nmtma.OA-2024-0050

Publication Date : 2024-10-08

  • Abstract

We construct first- and second-order time semi-discretization numerical schemes for the Cahn-Hilliard-Navier-Stokes model. This discretization scheme is based on the energy form of the scalar auxiliary variable approach for the coupling terms of model and pressure correction in the Navier-Stokes equations, which are fully decoupled. Then, we apply the fully explicit forms and the two scalar auxiliary variables to obtain stable unconditional energy over time. At the same time, we present the error analysis for the first-order scheme and the convergence rate for all relevant variables in different norms. Finally, numerical examples are presented to validate the theoretical analysis.

  • Copyright

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