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

Junxiang Yang; Zhijun Tan; Junseok Kim

doi:10.1016/j.compfluid.2022.105432

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 journal › Article › peer-review

8 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 language	English
Article number	105432
Journal	Computers and Fluids
Volume	240
DOIs	https://doi.org/10.1016/j.compfluid.2022.105432
Publication status	Published - 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

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10.1016/j.compfluid.2022.105432

Cite this

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

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.",

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author = "Junxiang Yang and Zhijun Tan and Junseok Kim",

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doi = "10.1016/j.compfluid.2022.105432",

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AU - Yang, Junxiang

AU - Tan, Zhijun

AU - Kim, Junseok

N1 - 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

PY - 2022/5/30

Y1 - 2022/5/30

N2 - 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.

AB - 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.

KW - Energy stability

KW - Lagrange multiplier method

KW - Navier–Stokes equation

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SN - 0045-7930

VL - 240

JO - Computers and Fluids

JF - Computers and Fluids

M1 - 105432

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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