Volume 3, Issue 1
Efficient and Unconditional Energy Stable Schemes for the Micropolar Navier-Stokes Equations

Jie Shen & Nan Zheng

CSIAM Trans. Appl. Math., 3 (2022), pp. 57-81.

Published online: 2022-03

Export citation
  • Abstract

We develop in this paper efficient numerical schemes for solving the micropolar Navier-Stokes equations by combining the SAV approach and pressure-correction method. Our first- and second-order semi-discrete schemes enjoy remarkable properties such as (i) unconditional energy stability with a modified energy, and (ii) only a sequence of decoupled linear equations with constant coefficients need to be solved at each time step. We also construct fully discrete versions of these schemes with a special spectral discretization which preserve the essential properties of the semi-discrete schemes. Numerical experiments are presented to validate the proposed schemes.

  • Keywords

Micropolar Navier-Stokes, pressure-correction, scalar auxiliary variable, energy stability.

  • AMS Subject Headings

65M12, 65M70, 35Q30, 76A05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CSIAM-AM-3-57, author = {Jie and Shen and and 22461 and and Jie Shen and Nan and Zheng and and 22462 and and Nan Zheng}, title = {Efficient and Unconditional Energy Stable Schemes for the Micropolar Navier-Stokes Equations}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2022}, volume = {3}, number = {1}, pages = {57--81}, abstract = {

We develop in this paper efficient numerical schemes for solving the micropolar Navier-Stokes equations by combining the SAV approach and pressure-correction method. Our first- and second-order semi-discrete schemes enjoy remarkable properties such as (i) unconditional energy stability with a modified energy, and (ii) only a sequence of decoupled linear equations with constant coefficients need to be solved at each time step. We also construct fully discrete versions of these schemes with a special spectral discretization which preserve the essential properties of the semi-discrete schemes. Numerical experiments are presented to validate the proposed schemes.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.SO-2021-0008}, url = {http://global-sci.org/intro/article_detail/csiam-am/20288.html} }
TY - JOUR T1 - Efficient and Unconditional Energy Stable Schemes for the Micropolar Navier-Stokes Equations AU - Shen , Jie AU - Zheng , Nan JO - CSIAM Transactions on Applied Mathematics VL - 1 SP - 57 EP - 81 PY - 2022 DA - 2022/03 SN - 3 DO - http://doi.org/10.4208/csiam-am.SO-2021-0008 UR - https://global-sci.org/intro/article_detail/csiam-am/20288.html KW - Micropolar Navier-Stokes, pressure-correction, scalar auxiliary variable, energy stability. AB -

We develop in this paper efficient numerical schemes for solving the micropolar Navier-Stokes equations by combining the SAV approach and pressure-correction method. Our first- and second-order semi-discrete schemes enjoy remarkable properties such as (i) unconditional energy stability with a modified energy, and (ii) only a sequence of decoupled linear equations with constant coefficients need to be solved at each time step. We also construct fully discrete versions of these schemes with a special spectral discretization which preserve the essential properties of the semi-discrete schemes. Numerical experiments are presented to validate the proposed schemes.

Jie Shen & Nan Zheng. (2022). Efficient and Unconditional Energy Stable Schemes for the Micropolar Navier-Stokes Equations. CSIAM Transactions on Applied Mathematics. 3 (1). 57-81. doi:10.4208/csiam-am.SO-2021-0008
Copy to clipboard
The citation has been copied to your clipboard