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Volume 18, Issue 1
Stability and Error Analysis of SAV Semi-Discrete Scheme for Cahn-Hilliard-Navier-Stokes Model

Haijun Gao, Xi Li & Minfu Feng

DOI: 10.4208/nmtma.OA-2024-0050

Numer. Math. Theor. Meth. Appl., 18 (2025), pp. 66-102.

Published online: 2025-04

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  • 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.

  • Keywords

Cahn-Hilliard-Navier-Stokes, fully decoupled, scalar auxiliary variable (SAV), energy stability, error estimates.

  • AMS Subject Headings

35Q30, 65M12, 65M60, 65P40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-18-66, author = {Gao , HaijunLi , Xi and Feng , Minfu}, title = {Stability and Error Analysis of SAV Semi-Discrete Scheme for Cahn-Hilliard-Navier-Stokes Model}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2025}, volume = {18}, number = {1}, pages = {66--102}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2024-0050}, url = {http://global-sci.org/intro/article_detail/nmtma/23942.html} }
TY - JOUR T1 - Stability and Error Analysis of SAV Semi-Discrete Scheme for Cahn-Hilliard-Navier-Stokes Model AU - Gao , Haijun AU - Li , Xi AU - Feng , Minfu JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 66 EP - 102 PY - 2025 DA - 2025/04 SN - 18 DO - http://doi.org/10.4208/nmtma.OA-2024-0050 UR - https://global-sci.org/intro/article_detail/nmtma/23942.html KW - Cahn-Hilliard-Navier-Stokes, fully decoupled, scalar auxiliary variable (SAV), energy stability, error estimates. AB -

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.

Gao , HaijunLi , Xi and Feng , Minfu. (2025). Stability and Error Analysis of SAV Semi-Discrete Scheme for Cahn-Hilliard-Navier-Stokes Model. Numerical Mathematics: Theory, Methods and Applications. 18 (1). 66-102. doi:10.4208/nmtma.OA-2024-0050
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