Volume 5, Issue 1
Two-Level Stabilized Finite Volume Methods for the Stationary Navier-Stokes Equations

Tong Zhang & Shunwei Xu

Adv. Appl. Math. Mech., 5 (2013), pp. 19-35.

Published online: 2013-05

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  • Abstract

In this work, two-level stabilized finite volume formulations for the 2D steady Navier-Stokes equations are considered. These methods are based on the local Gauss integration technique and the lowest equal-order finite element pair. Moreover, the two-level stabilized finite volume methods involve solving one small Navier-Stokes problem on a coarse mesh with mesh size H, a large general Stokes problem for the Simple and Oseen two-level stabilized finite volume methods on the fine mesh with mesh size h=O(H^2) or a large general Stokes equations for the Newton two-level stabilized finite volume method on a fine mesh with mesh size h=O(|\log h|^{1/2}H^3). These methods we studied provide an approximate solution (\widetilde{u}_h^v,\widetilde{p}_h^v) with the convergence rate of same order as the standard stabilized finite volume method, which involve solving one large nonlinear problem on a fine mesh with mesh size h. Hence, our methods can save a large amount of computational time.

  • Keywords

Stationary Navier-Stokes equations finite volume method two-level method error estimate

  • AMS Subject Headings

65N30 65N08 76D05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-5-19, author = {Tong Zhang and Shunwei Xu}, title = {Two-Level Stabilized Finite Volume Methods for the Stationary Navier-Stokes Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2013}, volume = {5}, number = {1}, pages = {19--35}, abstract = {

In this work, two-level stabilized finite volume formulations for the 2D steady Navier-Stokes equations are considered. These methods are based on the local Gauss integration technique and the lowest equal-order finite element pair. Moreover, the two-level stabilized finite volume methods involve solving one small Navier-Stokes problem on a coarse mesh with mesh size H, a large general Stokes problem for the Simple and Oseen two-level stabilized finite volume methods on the fine mesh with mesh size h=O(H^2) or a large general Stokes equations for the Newton two-level stabilized finite volume method on a fine mesh with mesh size h=O(|\log h|^{1/2}H^3). These methods we studied provide an approximate solution (\widetilde{u}_h^v,\widetilde{p}_h^v) with the convergence rate of same order as the standard stabilized finite volume method, which involve solving one large nonlinear problem on a fine mesh with mesh size h. Hence, our methods can save a large amount of computational time.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.11-m11178}, url = {http://global-sci.org/intro/article_detail/aamm/55.html} }
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