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

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

Keywords

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

ASJC Scopus subject areas

  • Computer Science(all)
  • Engineering(all)

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