TY - JOUR
T1 - Original variables based energy-stable time-dependent auxiliary variable method for the incompressible Navier–Stokes equation
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
UR - http://www.scopus.com/inward/record.url?scp=85127578049&partnerID=8YFLogxK
U2 - 10.1016/j.compfluid.2022.105432
DO - 10.1016/j.compfluid.2022.105432
M3 - Article
AN - SCOPUS:85127578049
SN - 0045-7930
VL - 240
JO - Computers and Fluids
JF - Computers and Fluids
M1 - 105432
ER -