Volume 6, Issue 5
A New Finite Volume Element Formulation for the Non-Stationary Navier-Stokes Equations

Zhendong Luo

Adv. Appl. Math. Mech., 6 (2014), pp. 615-636.

Published online: 2014-06

Preview Full PDF 1 752
Export citation
  • Abstract

A semi-discrete scheme about time for the non-stationary Navier-Stokes equations is presented firstly, then a new fully discrete finite volume element (FVE) formulation based on macroelement is directly established from the semi-discrete scheme about time. And the error estimates for the fully discrete FVE solutions are derived by means of the technique of the standard finite element method. It is shown by numerical experiments that the numerical results are consistent with theoretical conclusions. Moreover, it is shown that the FVE method is feasible and efficient for finding the numerical solutions of the non-stationary Navier-Stokes equations and it is one of the most effective numerical methods among the FVE formulation, the finite element formulation, and the finite difference scheme.

  • Keywords

Non-stationary Navier-Stokes equations finite volumes element method error estimate numerical simulations

  • AMS Subject Headings

65N30 65M30 76M10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAMM-6-615, author = {Zhendong Luo}, title = {A New Finite Volume Element Formulation for the Non-Stationary Navier-Stokes Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2014}, volume = {6}, number = {5}, pages = {615--636}, abstract = {

A semi-discrete scheme about time for the non-stationary Navier-Stokes equations is presented firstly, then a new fully discrete finite volume element (FVE) formulation based on macroelement is directly established from the semi-discrete scheme about time. And the error estimates for the fully discrete FVE solutions are derived by means of the technique of the standard finite element method. It is shown by numerical experiments that the numerical results are consistent with theoretical conclusions. Moreover, it is shown that the FVE method is feasible and efficient for finding the numerical solutions of the non-stationary Navier-Stokes equations and it is one of the most effective numerical methods among the FVE formulation, the finite element formulation, and the finite difference scheme.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m83}, url = {http://global-sci.org/intro/article_detail/aamm/39.html} }
TY - JOUR T1 - A New Finite Volume Element Formulation for the Non-Stationary Navier-Stokes Equations AU - Zhendong Luo JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 615 EP - 636 PY - 2014 DA - 2014/06 SN - 6 DO - http://dor.org/10.4208/aamm.2013.m83 UR - https://global-sci.org/intro/aamm/39.html KW - Non-stationary Navier-Stokes equations KW - finite volumes element method KW - error estimate KW - numerical simulations AB -

A semi-discrete scheme about time for the non-stationary Navier-Stokes equations is presented firstly, then a new fully discrete finite volume element (FVE) formulation based on macroelement is directly established from the semi-discrete scheme about time. And the error estimates for the fully discrete FVE solutions are derived by means of the technique of the standard finite element method. It is shown by numerical experiments that the numerical results are consistent with theoretical conclusions. Moreover, it is shown that the FVE method is feasible and efficient for finding the numerical solutions of the non-stationary Navier-Stokes equations and it is one of the most effective numerical methods among the FVE formulation, the finite element formulation, and the finite difference scheme.

Zhendong Luo. (1970). A New Finite Volume Element Formulation for the Non-Stationary Navier-Stokes Equations. Advances in Applied Mathematics and Mechanics. 6 (5). 615-636. doi:10.4208/aamm.2013.m83
Copy to clipboard
The citation has been copied to your clipboard