Numerical verification of stationary solutions for Navier-Stokes problems

K. Nagatou; K. Hashimoto; M. T. Nakao

doi:10.1016/j.cam.2005.09.031

Numerical verification of stationary solutions for Navier-Stokes problems

K. Nagatou, K. Hashimoto, M. T. Nakao

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

We present a numerical method to enclose stationary solutions of the Navier-Stokes equations, especially 2-D driven cavity problem with regularized boundary condition. Our method is based on the infinite dimensional Newton's method by estimating the inverse of the corresponding linearized operator. The method can be applied to the case for high Reynolds numbers and we show some numerical examples which confirm us the actual effectiveness.

Original language	English
Pages (from-to)	445-451
Number of pages	7
Journal	Journal of Computational and Applied Mathematics
Volume	199
Issue number	2
DOIs	https://doi.org/10.1016/j.cam.2005.09.031
Publication status	Published - 2007 Feb 15
Externally published	Yes

Keywords

Driven cavity flows
Infinite dimensional Newton's method
Numerical enclosure method

ASJC Scopus subject areas

Applied Mathematics
Computational Mathematics
Numerical Analysis

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abstract = "We present a numerical method to enclose stationary solutions of the Navier-Stokes equations, especially 2-D driven cavity problem with regularized boundary condition. Our method is based on the infinite dimensional Newton's method by estimating the inverse of the corresponding linearized operator. The method can be applied to the case for high Reynolds numbers and we show some numerical examples which confirm us the actual effectiveness.",

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AU - Hashimoto, K.

AU - Nakao, M. T.

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N2 - We present a numerical method to enclose stationary solutions of the Navier-Stokes equations, especially 2-D driven cavity problem with regularized boundary condition. Our method is based on the infinite dimensional Newton's method by estimating the inverse of the corresponding linearized operator. The method can be applied to the case for high Reynolds numbers and we show some numerical examples which confirm us the actual effectiveness.

AB - We present a numerical method to enclose stationary solutions of the Navier-Stokes equations, especially 2-D driven cavity problem with regularized boundary condition. Our method is based on the infinite dimensional Newton's method by estimating the inverse of the corresponding linearized operator. The method can be applied to the case for high Reynolds numbers and we show some numerical examples which confirm us the actual effectiveness.

KW - Driven cavity flows

KW - Infinite dimensional Newton's method

KW - Numerical enclosure method

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