Binary thermal fluids computation over arbitrary surfaces with second-order accuracy and unconditional energy stability based on phase-field model

Qing Xia, Yuehan Liu, Junseok Kim, Yibao Li

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

In this paper, we propose an efficient surface computational system with second-order spatial and temporal accuracy to solve multiple physical field coupling problems over arbitrary surfaces. The computational system is coupled with heat transfer equation and incompressible Navier–Stokes equation based on a phase-field model. Due to the discretization of the triangular grids, we define the discretized gradient operator, divergence operator and the Laplace–Beltrami operator with second-order spatial accuracy. The Crank–Nicolson-type scheme is used to confirm the temporal accuracy. The Navier–Stokes equation is solved by the projection method. We use the biconjugate gradient stabilized method to solve the involved equations. The discrete system is provable to be unconditionally stable and the mass conservation law is satisfied during the computation, which implies that the proposed method is not limited by the temporal step. Several computational tests are conducted to show the efficiency, robustness and accuracy of the proposed scheme.

Original languageEnglish
Article number115319
JournalJournal of Computational and Applied Mathematics
Volume433
DOIs
Publication statusPublished - 2023 Dec 1

Bibliographical note

Funding Information:
The corresponding author (Y.B. Li) is supported by National Natural Science Foundation of China (No. 12271430 ). Q. Xia is supported by the Fundamental Research Funds for the Central Universities, China (No. XYZ022022005 ). J.S. Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2019R1A2C1003053 ). The authors would like to thank the reviewers for their constructive and helpful comments regarding the revision of this article.

Publisher Copyright:
© 2023 Elsevier B.V.

Keywords

  • Heat convection
  • Laplace–Beltrami operator
  • Multiple physical field coupling
  • Second-order accuracy
  • Two-phase flow
  • Unconditional energy stability

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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