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Volume 8, Issue 3
On an Unconditionally Stable Scheme for the Unsteady Navier-Stokes Equations

Jie Shen

J. Comp. Math., 8 (1990), pp. 276-288.

Published online: 1990-08

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  • Abstract

Theoretical time step constraints of semi-implicit schemes are known to be more restrictive than should be in practice. We intend to alleviate the constraints with more smoothness assumptions on the solutions. By introducing a new scheme with modification on the treatment of the nonlinear term, we are able to prove that the scheme is unconditionally stable and convergent. Furthermore, we show that the modified scheme and the original semi-implicit one are equivalent under a weak condition on the time step and the number of space discretization points.

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@Article{JCM-8-276, author = {Jie Shen}, title = {On an Unconditionally Stable Scheme for the Unsteady Navier-Stokes Equations}, journal = {Journal of Computational Mathematics}, year = {1990}, volume = {8}, number = {3}, pages = {276--288}, abstract = {

Theoretical time step constraints of semi-implicit schemes are known to be more restrictive than should be in practice. We intend to alleviate the constraints with more smoothness assumptions on the solutions. By introducing a new scheme with modification on the treatment of the nonlinear term, we are able to prove that the scheme is unconditionally stable and convergent. Furthermore, we show that the modified scheme and the original semi-implicit one are equivalent under a weak condition on the time step and the number of space discretization points.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9440.html} }
TY - JOUR T1 - On an Unconditionally Stable Scheme for the Unsteady Navier-Stokes Equations AU - Jie Shen JO - Journal of Computational Mathematics VL - 3 SP - 276 EP - 288 PY - 1990 DA - 1990/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9440.html KW - AB -

Theoretical time step constraints of semi-implicit schemes are known to be more restrictive than should be in practice. We intend to alleviate the constraints with more smoothness assumptions on the solutions. By introducing a new scheme with modification on the treatment of the nonlinear term, we are able to prove that the scheme is unconditionally stable and convergent. Furthermore, we show that the modified scheme and the original semi-implicit one are equivalent under a weak condition on the time step and the number of space discretization points.

Jie Shen. (1990). On an Unconditionally Stable Scheme for the Unsteady Navier-Stokes Equations. Journal of Computational Mathematics. 8 (3). 276-288. doi:
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