Iterative projection method for unsteady Navier-Stokes equations with high Reynolds numbers
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918151787118592 |
|---|---|
| author | Zheng, Xiaoming Zhao, Kun Wu, Jiahong Hu, Weiwei Du, Dapeng |
| author_facet | Zheng, Xiaoming Zhao, Kun Wu, Jiahong Hu, Weiwei Du, Dapeng |
| contents | A new iterative projection method is proposed to solve the unsteady Navier-Stokes equations with high Reynolds numbers. The convectional projection method attempts to project the intermediate velocity to the divergence free space only once per time step. However, such a velocity is not genuinely divergence free in general practice, which can yield large errors when the Reynolds number is high. The new method has several important features: the BDF2 time discretization, the skew-symmetric convection in a semi-implicit form, two modulating parameters, and the iterative projections in each time step. A major difficulty in the proof of iteration convergence is the nonlinear convection. We solve this problem by first analyzing the non-convective scheme with a focus on the spectral properties of the iterative matrix, and then employing a delicate perturbation analysis for the convective scheme. The work achieves the weakly divergence free velocity (strongly divergence free for divergence free finite element spaces), and the rigorous stability and error analysis when the iterations converge. The three dimensional numerical tests confirm that this new method can effectively treat high Reynolds numbers with only a few iterations per time step, where the convectional projection method and the iterative projection method with the explicit convection would fail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_07963 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Iterative projection method for unsteady Navier-Stokes equations with high Reynolds numbers Zheng, Xiaoming Zhao, Kun Wu, Jiahong Hu, Weiwei Du, Dapeng Numerical Analysis 65M60 A new iterative projection method is proposed to solve the unsteady Navier-Stokes equations with high Reynolds numbers. The convectional projection method attempts to project the intermediate velocity to the divergence free space only once per time step. However, such a velocity is not genuinely divergence free in general practice, which can yield large errors when the Reynolds number is high. The new method has several important features: the BDF2 time discretization, the skew-symmetric convection in a semi-implicit form, two modulating parameters, and the iterative projections in each time step. A major difficulty in the proof of iteration convergence is the nonlinear convection. We solve this problem by first analyzing the non-convective scheme with a focus on the spectral properties of the iterative matrix, and then employing a delicate perturbation analysis for the convective scheme. The work achieves the weakly divergence free velocity (strongly divergence free for divergence free finite element spaces), and the rigorous stability and error analysis when the iterations converge. The three dimensional numerical tests confirm that this new method can effectively treat high Reynolds numbers with only a few iterations per time step, where the convectional projection method and the iterative projection method with the explicit convection would fail. |
| title | Iterative projection method for unsteady Navier-Stokes equations with high Reynolds numbers |
| topic | Numerical Analysis 65M60 |
| url | https://arxiv.org/abs/2304.07963 |