New High-Order Numerical Methods for Hyperbolic Systems of Nonlinear PDEs with Uncertainties
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929408672006144 |
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| author | Chertock, Alina Herty, Michael Iskhakov, Arsen S. Janajra, Safa Kurganov, Alexander Lukacova-Medvidova, Maria |
| author_facet | Chertock, Alina Herty, Michael Iskhakov, Arsen S. Janajra, Safa Kurganov, Alexander Lukacova-Medvidova, Maria |
| contents | In this paper, we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations (PDEs) with uncertainties. The new approach is realized in the semi-discrete finite-volume framework and is based on fifth-order weighted essentially non-oscillatory (WENO) interpolations in (multidimensional) random space combined with second-order piecewise linear reconstruction in physical space. Compared with spectral approximations in the random space, the presented methods are essentially non-oscillatory as they do not suffer from the Gibbs phenomenon while still achieving high-order accuracy. The new methods are tested on a number of numerical examples for both the Euler equations of gas dynamics and the Saint-Venant system of shallow-water equations. In the latter case, the methods are also proven to be well-balanced and positivity-preserving. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08280 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | New High-Order Numerical Methods for Hyperbolic Systems of Nonlinear PDEs with Uncertainties Chertock, Alina Herty, Michael Iskhakov, Arsen S. Janajra, Safa Kurganov, Alexander Lukacova-Medvidova, Maria Numerical Analysis In this paper, we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations (PDEs) with uncertainties. The new approach is realized in the semi-discrete finite-volume framework and is based on fifth-order weighted essentially non-oscillatory (WENO) interpolations in (multidimensional) random space combined with second-order piecewise linear reconstruction in physical space. Compared with spectral approximations in the random space, the presented methods are essentially non-oscillatory as they do not suffer from the Gibbs phenomenon while still achieving high-order accuracy. The new methods are tested on a number of numerical examples for both the Euler equations of gas dynamics and the Saint-Venant system of shallow-water equations. In the latter case, the methods are also proven to be well-balanced and positivity-preserving. |
| title | New High-Order Numerical Methods for Hyperbolic Systems of Nonlinear PDEs with Uncertainties |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2312.08280 |