A New Reduced Stabilized Mixed Finite-Element Method Based on Proper Orthogonal Decomposition for the Transient Navier-Stokes Equations

Aiwen Wang, Jian Li, Zhenhua Di, Xiangjun Tian and Dongxiu Xie

Mathematical Problems in Engineering, 2011, vol. 2011, 1-19

Abstract:

A reduced stabilized mixed finite-element (RSMFE) formulation based on proper orthogonal decomposition (POD) for the transient Navier-Stokes equations is presented. An ensemble of snapshots is compiled from the transient solutions derived from a stabilized mixed finite-element (SMFE) method based on two local Gauss integrations for the two-dimensional transient Navier-Stokes equations by using the lowest equal-order pair of finite elements. Then, the optimal orthogonal bases are reconstructed by implementing POD techniques for the ensemble snapshots. Combining POD with the SMFE formulation, a new low-dimensional and highly accurate SMFE method for the transient Navier-Stokes equations is obtained. The RSMFE formulation could not only greatly reduce its degrees of freedom but also circumvent the constraint of inf-sup stability condition. Error estimates between the SMFE solutions and the RSMFE solutions are derived. Numerical tests confirm that the errors between the RSMFE solutions and the SMFE solutions are consistent with the the theoretical results. Conclusion can be drawn that RSMFE method is feasible and efficient for solving the transient Navier-Stokes equations.

Date: 2011
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/MPE/2011/895386.pdf (application/pdf)
http://downloads.hindawi.com/journals/MPE/2011/895386.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:895386

DOI: 10.1155/2011/895386

Access Statistics for this article

More articles in Mathematical Problems in Engineering from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().