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 | |
| 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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Cite this
Nagatou, K., Hashimoto, K., & Nakao, M. T. (2007). Numerical verification of stationary solutions for Navier-Stokes problems. Journal of Computational and Applied Mathematics, 199(2), 445-451. https://doi.org/10.1016/j.cam.2005.09.031