An Asymptotic Preserving and Energy Stable Scheme for the Euler System with Congestion Constraint
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916295804452864 |
|---|---|
| author | Arun, K. R. Krishnamurthy, Amogh Maharana, Harihara |
| author_facet | Arun, K. R. Krishnamurthy, Amogh Maharana, Harihara |
| contents | In this work, we design and analyze an asymptotic preserving (AP), semi-implicit finite volume scheme for the scaled compressible isentropic Euler system with a singular pressure law known as the congestion pressure law. The congestion pressure law imposes a maximal density constraint of the form $0\leq \varrho <1$, and the scaling introduces a small parameter $\varepsilon$ in order to control the stiffness of the density constraint. As $\varepsilon\to 0$, the solutions of the compressible system converge to solutions of the so-called free-congested Euler equations that couples compressible and incompressible dynamics. We show that the proposed scheme is positivity preserving and energy stable. In addition, we also show that the numerical densities satisfy a discrete variant of the constraint. By means of extensive numerical case studies, we verify the efficacy of the scheme and show that the scheme is able to capture the two dynamics in the limiting regime, thereby proving the AP property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14168 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Asymptotic Preserving and Energy Stable Scheme for the Euler System with Congestion Constraint Arun, K. R. Krishnamurthy, Amogh Maharana, Harihara Numerical Analysis 35L65, 35Q31, 65M08, 76M12 In this work, we design and analyze an asymptotic preserving (AP), semi-implicit finite volume scheme for the scaled compressible isentropic Euler system with a singular pressure law known as the congestion pressure law. The congestion pressure law imposes a maximal density constraint of the form $0\leq \varrho <1$, and the scaling introduces a small parameter $\varepsilon$ in order to control the stiffness of the density constraint. As $\varepsilon\to 0$, the solutions of the compressible system converge to solutions of the so-called free-congested Euler equations that couples compressible and incompressible dynamics. We show that the proposed scheme is positivity preserving and energy stable. In addition, we also show that the numerical densities satisfy a discrete variant of the constraint. By means of extensive numerical case studies, we verify the efficacy of the scheme and show that the scheme is able to capture the two dynamics in the limiting regime, thereby proving the AP property. |
| title | An Asymptotic Preserving and Energy Stable Scheme for the Euler System with Congestion Constraint |
| topic | Numerical Analysis 35L65, 35Q31, 65M08, 76M12 |
| url | https://arxiv.org/abs/2406.14168 |