A high-order accurate unconditionally stable bound-preserving numerical scheme for the Cahn-Hilliard-Navier-Stokes equations

Yali Gao; Daozhi Han; Sayantan Sarkar

doi:10.1016/j.apnum.2025.06.004

A high-order accurate unconditionally stable bound-preserving numerical scheme for the Cahn-Hilliard-Navier-Stokes equations

Yali Gao
, Daozhi Han
, Sayantan Sarkar

Mathematics

Northwestern Polytechnical University Xian
SUNY Buffalo

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

A high order numerical method is developed for solving the Cahn-Hilliard-Navier-Stokes equations with the Flory-Huggins potential. The scheme is based on the Q_k finite element with mass lumping on rectangular grids, the second-order convex splitting method and the pressure correction method. The unique solvability, unconditional stability, and bound-preserving properties are rigorously established. The key for bound-preservation is the discrete L¹ estimate of the singular potential. Ample numerical experiments are performed to validate the desired properties of the proposed numerical scheme.

Original language	English
Pages (from-to)	96-111
Number of pages	16
Journal	Applied Numerical Mathematics
Volume	217
DOIs	https://doi.org/10.1016/j.apnum.2025.06.004
State	Published - Nov 2025

Keywords

Bound-preserving
Cahn-Hilliard-Navier-Stokes
Flory-Huggin potential
High order accuracy
Quadrilateral element
Unique solvability

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10.1016/j.apnum.2025.06.004

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title = "A high-order accurate unconditionally stable bound-preserving numerical scheme for the Cahn-Hilliard-Navier-Stokes equations",

abstract = "A high order numerical method is developed for solving the Cahn-Hilliard-Navier-Stokes equations with the Flory-Huggins potential. The scheme is based on the Qk finite element with mass lumping on rectangular grids, the second-order convex splitting method and the pressure correction method. The unique solvability, unconditional stability, and bound-preserving properties are rigorously established. The key for bound-preservation is the discrete L1 estimate of the singular potential. Ample numerical experiments are performed to validate the desired properties of the proposed numerical scheme.",

keywords = "Bound-preserving, Cahn-Hilliard-Navier-Stokes, Flory-Huggin potential, High order accuracy, Quadrilateral element, Unique solvability",

author = "Yali Gao and Daozhi Han and Sayantan Sarkar",

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year = "2025",

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doi = "10.1016/j.apnum.2025.06.004",

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T1 - A high-order accurate unconditionally stable bound-preserving numerical scheme for the Cahn-Hilliard-Navier-Stokes equations

AU - Gao, Yali

AU - Han, Daozhi

AU - Sarkar, Sayantan

PY - 2025/11

Y1 - 2025/11

N2 - A high order numerical method is developed for solving the Cahn-Hilliard-Navier-Stokes equations with the Flory-Huggins potential. The scheme is based on the Qk finite element with mass lumping on rectangular grids, the second-order convex splitting method and the pressure correction method. The unique solvability, unconditional stability, and bound-preserving properties are rigorously established. The key for bound-preservation is the discrete L1 estimate of the singular potential. Ample numerical experiments are performed to validate the desired properties of the proposed numerical scheme.

AB - A high order numerical method is developed for solving the Cahn-Hilliard-Navier-Stokes equations with the Flory-Huggins potential. The scheme is based on the Qk finite element with mass lumping on rectangular grids, the second-order convex splitting method and the pressure correction method. The unique solvability, unconditional stability, and bound-preserving properties are rigorously established. The key for bound-preservation is the discrete L1 estimate of the singular potential. Ample numerical experiments are performed to validate the desired properties of the proposed numerical scheme.

KW - Bound-preserving

KW - Cahn-Hilliard-Navier-Stokes

KW - Flory-Huggin potential

KW - High order accuracy

KW - Quadrilateral element

KW - Unique solvability

UR - https://www.scopus.com/pages/publications/105007831167

U2 - 10.1016/j.apnum.2025.06.004

DO - 10.1016/j.apnum.2025.06.004

M3 - Article

AN - SCOPUS:105007831167

SN - 0168-9274

VL - 217

SP - 96

EP - 111

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

A high-order accurate unconditionally stable bound-preserving numerical scheme for the Cahn-Hilliard-Navier-Stokes equations

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Keywords

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