Solving Random Hyperbolic Conservation Laws Using Linear Programming
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912673096007680 |
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| author | Chu, Shaoshuai Herty, Michael Lukacova-Medvidova, Maria Zhou, Yizhou |
| author_facet | Chu, Shaoshuai Herty, Michael Lukacova-Medvidova, Maria Zhou, Yizhou |
| contents | A novel structure-preserving numerical method to solve random hyperbolic systems of conservation laws is presented. The method uses a concept of generalized, measure-valued solutions to random conservation laws. This yields a linear partial differential equation with respect to the Young measure and allows to compute the approximation based on linear programming problems. We analyze structure-preserving properties of the derived numerical method and discuss its advantages and disadvantages. We numerically demonstrate the approach on the one-dimensional Burgers and isentropic Euler equations and compare with stochastic collocation. In addition, we introduce a discontinuous-flux test in which different entropies used in the linear-program objective select different weak entropy solutions, and we report the corresponding changes in the moments and supports of the Young measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10104 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solving Random Hyperbolic Conservation Laws Using Linear Programming Chu, Shaoshuai Herty, Michael Lukacova-Medvidova, Maria Zhou, Yizhou Numerical Analysis A novel structure-preserving numerical method to solve random hyperbolic systems of conservation laws is presented. The method uses a concept of generalized, measure-valued solutions to random conservation laws. This yields a linear partial differential equation with respect to the Young measure and allows to compute the approximation based on linear programming problems. We analyze structure-preserving properties of the derived numerical method and discuss its advantages and disadvantages. We numerically demonstrate the approach on the one-dimensional Burgers and isentropic Euler equations and compare with stochastic collocation. In addition, we introduce a discontinuous-flux test in which different entropies used in the linear-program objective select different weak entropy solutions, and we report the corresponding changes in the moments and supports of the Young measure. |
| title | Solving Random Hyperbolic Conservation Laws Using Linear Programming |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2501.10104 |