A reduced-order least squares-support vector regression and isogeometric collocation method to simulate Cahn-Hilliard-Navier-Stokes equation

Abbaszadeh, Mostafa; Khodadadian, Amirreza; Parvizi, Maryam; Dehghan, Mehdi; Xiao, Dunhui

Abstract

The coupled Cahn-Hilliard-Navier-Stokes equations are employed to model two-phase flow separation. To enhance computational efficiency, the pressure term is eliminated from the system of equations, leveraging the stream and vorticity functions along with the momentum conservation equation. This procedure results in five equations with five unknowns. Subsequently, a second-order accurate time-discrete scheme is devised, treating each time step as a differential equation. The approach integrates least squares support vector regression with non-uniform rational B-spline (NURBS) basis functions, utilizing orthogonal bases. Additionally, a reduced-order model is proposed through proper orthogonal decomposition, contributing to a reduction in CPU time requirements. The effectiveness of the new numerical procedure is demonstrated through testing on well-known benchmark problems.

Citation

Abbaszadeh, M., Khodadadian, A., Parvizi, M., Dehghan, M., & Xiao, D. (2025). A reduced-order least squares-support vector regression and isogeometric collocation method to simulate Cahn-Hilliard-Navier-Stokes equation. Journal of Computational Physics, 523, Article 113650. https://doi.org/10.1016/j.jcp.2024.113650

• Journal Article Type: Article
• Acceptance Date: Dec 2, 2024
• Online Publication Date: Dec 5, 2024
• Publication Date: Feb 15, 2025
• Deposit Date: Feb 25, 2025
• Journal: Journal of Computational Physics
• Print ISSN: 0021-9991
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 523
• Article Number: 113650
• DOI: https://doi.org/10.1016/j.jcp.2024.113650
• Keywords: Cahn-Hilliard-Navier-Stokes equation; Isogeometric collocation method; Proper orthogonal decomposition method; Least squares support vector regression
• Public URL: https://keele-repository.worktribe.com/output/1015903
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0021999124008982?via%3Dihub