Original variables based energy-stable time-dependent auxiliary variable method for the incompressible Navier–Stokes equation

Junxiang Yang, Zhijun Tan, Junseok Kim

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

In this study, we develop an efficiently linear and energy-stable method for the incompressible Navier–Stokes equation. A time-dependent Lagrange multiplier is introduced to change the original equation into an equivalent form. Using the equivalent equation, we design a second-order time-accurate scheme based on the second-order backward difference formula (BDF2). The proposed scheme explicitly treats the advection term. In each time iteration, some linear elliptic type equations need to be solved. Therefore, the calculation is highly efficient. Moreover, the time-discretized energy stability with respect to original variables can be easily proved. Various benchmark tests, such as lid-driven cavity flow, Kelvin–Helmholtz instability, and Taylor–Green vortices, are performed to validate the performance of the proposed method.

Original languageEnglish
Article number105432
JournalComputers and Fluids
Volume240
DOIs
Publication statusPublished - 2022 May 30

Bibliographical note

Funding Information:
The work of Z. Tan is supported by the National Nature Science Foundation of China ( 11971502 ), and Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University ( 2020B1212060032 ). The corresponding author (J.S. Kim) was supported by Korea University Grant . The authors thank the reviewers for constructive and helpful comments on the revision of this article.

Publisher Copyright:
© 2022 Elsevier Ltd

Keywords

  • Energy stability
  • Lagrange multiplier method
  • Navier–Stokes equation

ASJC Scopus subject areas

  • General Computer Science
  • General Engineering

Fingerprint

Dive into the research topics of 'Original variables based energy-stable time-dependent auxiliary variable method for the incompressible Navier–Stokes equation'. Together they form a unique fingerprint.

Cite this