Intrinsic phenomena of delta shock waves in a more realistic Chaplygin Aw-Rascle model
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916890710900736 |
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| author | Priyanka Zafar, M. |
| author_facet | Priyanka Zafar, M. |
| contents | The motivation of this study is to find the Riemann solutions of the Aw-Rascle model with a more realistic version of extended Chaplygin gas. Firstly, we establish the Riemann solutions with two different structures, viz., a shock wave followed by the contact discontinuity and a rarefaction wave followed by the contact discontinuity. Further, by analyzing the limiting behavior, it is found that one of the Riemann solutions converges to a $ δ$-shock solution as the pressure approaches the generalized Chaplygin gas pressure. Moreover, numerical simulations have been performed to validate the theoretical analysis. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_12318 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Intrinsic phenomena of delta shock waves in a more realistic Chaplygin Aw-Rascle model Priyanka Zafar, M. Analysis of PDEs 35L03, 35L40, 35L65, 35L67 The motivation of this study is to find the Riemann solutions of the Aw-Rascle model with a more realistic version of extended Chaplygin gas. Firstly, we establish the Riemann solutions with two different structures, viz., a shock wave followed by the contact discontinuity and a rarefaction wave followed by the contact discontinuity. Further, by analyzing the limiting behavior, it is found that one of the Riemann solutions converges to a $ δ$-shock solution as the pressure approaches the generalized Chaplygin gas pressure. Moreover, numerical simulations have been performed to validate the theoretical analysis. |
| title | Intrinsic phenomena of delta shock waves in a more realistic Chaplygin Aw-Rascle model |
| topic | Analysis of PDEs 35L03, 35L40, 35L65, 35L67 |
| url | https://arxiv.org/abs/2406.12318 |