Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.14254 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910615371513856 |
|---|---|
| author | Fan, Yiyun Billingham, John van der Zee, Kristoffer |
| author_facet | Fan, Yiyun Billingham, John van der Zee, Kristoffer |
| contents | We develop a shape-Newton method for solving generic free-boundary problems where one of the free-boundary conditions is governed by the Bernoulli equation. The Newton-like scheme is developed by employing shape derivatives in the weak forms, which allows us to update the position of the free surface and the potential on the free boundary by solving a boundary-value problem at each iteration. To validate the effectiveness of the approach, we apply the scheme to solve a problem involving the flow over a submerged triangular obstacle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_14254 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Shape-Newton Method for Free-boundary Problems Subject to The Bernoulli Boundary Condition Fan, Yiyun Billingham, John van der Zee, Kristoffer Numerical Analysis We develop a shape-Newton method for solving generic free-boundary problems where one of the free-boundary conditions is governed by the Bernoulli equation. The Newton-like scheme is developed by employing shape derivatives in the weak forms, which allows us to update the position of the free surface and the potential on the free boundary by solving a boundary-value problem at each iteration. To validate the effectiveness of the approach, we apply the scheme to solve a problem involving the flow over a submerged triangular obstacle. |
| title | A Shape-Newton Method for Free-boundary Problems Subject to The Bernoulli Boundary Condition |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2305.14254 |