Non-diffusive neural network method for hyperbolic conservation laws
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916259339173888 |
|---|---|
| author | Lorin, Emmanuel Novruzi, Arian |
| author_facet | Lorin, Emmanuel Novruzi, Arian |
| contents | In this paper we develop a non-diffusive neural network (NDNN) algorithm for accurately solving weak solutions to hyperbolic conservation laws. The principle is to construct these weak solutions by computing smooth local solutions in subdomains bounded by discontinuity lines (DLs), the latter defined from the Rankine-Hugoniot jump conditions. The proposed approach allows to efficiently consider an arbitrary number of entropic shock waves, shock wave generation, as well as wave interactions. Some numerical experiments are presented to illustrate the strengths and properties of the algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15559 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-diffusive neural network method for hyperbolic conservation laws Lorin, Emmanuel Novruzi, Arian Numerical Analysis 35A35, 35L02, 35L65, 35D30, 65M55 In this paper we develop a non-diffusive neural network (NDNN) algorithm for accurately solving weak solutions to hyperbolic conservation laws. The principle is to construct these weak solutions by computing smooth local solutions in subdomains bounded by discontinuity lines (DLs), the latter defined from the Rankine-Hugoniot jump conditions. The proposed approach allows to efficiently consider an arbitrary number of entropic shock waves, shock wave generation, as well as wave interactions. Some numerical experiments are presented to illustrate the strengths and properties of the algorithms. |
| title | Non-diffusive neural network method for hyperbolic conservation laws |
| topic | Numerical Analysis 35A35, 35L02, 35L65, 35D30, 65M55 |
| url | https://arxiv.org/abs/2405.15559 |