Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes for Shallow Water Linearized Moment Equations
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916765594812416 |
|---|---|
| author | Cao, Yangyang Huang, Qian Koellermeier, Julian Kurganov, Alexander Liu, Yongle |
| author_facet | Cao, Yangyang Huang, Qian Koellermeier, Julian Kurganov, Alexander Liu, Yongle |
| contents | We develop second-order path-conservative central-upwind (PCCU) schemes for the hyperbolic shallow water linearized moment equations (HSWLME), which are an extension of standard depth-averaged models for free-surface flows. The proposed PCCU schemes are constructed via flux globalization strategies adapted to the nonconservative form via a path-conservative finite-volume method. The resulting scheme is well-balanced (WB) in the sense that it is capable of exactly preserving physically relevant steady states including moving-water ones. We validate the proposed scheme on several benchmarks, including smooth solutions, small perturbation of steady states, and dam-break scenarios. These results demonstrate that our flux globalization based WB PCCU schemes provide a reliable framework for computing solutions of shallow water moment models with nonlinear and nonconservative features. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23144 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes for Shallow Water Linearized Moment Equations Cao, Yangyang Huang, Qian Koellermeier, Julian Kurganov, Alexander Liu, Yongle Numerical Analysis We develop second-order path-conservative central-upwind (PCCU) schemes for the hyperbolic shallow water linearized moment equations (HSWLME), which are an extension of standard depth-averaged models for free-surface flows. The proposed PCCU schemes are constructed via flux globalization strategies adapted to the nonconservative form via a path-conservative finite-volume method. The resulting scheme is well-balanced (WB) in the sense that it is capable of exactly preserving physically relevant steady states including moving-water ones. We validate the proposed scheme on several benchmarks, including smooth solutions, small perturbation of steady states, and dam-break scenarios. These results demonstrate that our flux globalization based WB PCCU schemes provide a reliable framework for computing solutions of shallow water moment models with nonlinear and nonconservative features. |
| title | Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes for Shallow Water Linearized Moment Equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2505.23144 |