Numerical Study of Dissipative Weak Solutions for the Euler Equations of Gas Dynamics
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910001627398144 |
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| author | Chu, Shaoshuai Herty, Michael Kurganov, Alexander Lukacova-Medvidova, Maria Yu, Changsheng |
| author_facet | Chu, Shaoshuai Herty, Michael Kurganov, Alexander Lukacova-Medvidova, Maria Yu, Changsheng |
| contents | We study dissipative weak (DW) solutions of the Euler equations of gas dynamics using the first-, second-, third-, fifth-, seventh-, and ninth-order local characteristic decomposition-based central-upwind (LCDCU), low-dissipation central-upwind (LDCU), and viscous finite volume (VFV) methods, whose higher-order extensions are obtained via the framework of the alternative weighted essentially non-oscillatory (A-WENO) schemes. These methods are applied to several benchmark problems, including several two-dimensional Riemann problems and a Kelvin-Helmholtz instability test. The numerical results demonstrate that for methods converging only weakly in space and time, the limiting solutions are generalized DW solutions, approximated in the sense of ${\cal K}$-convergence and dependent on the numerical scheme. For all of the studied methods, we compute the associated Young measures and compare the DW solutions using entropy production and energy defect criteria. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_17452 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Numerical Study of Dissipative Weak Solutions for the Euler Equations of Gas Dynamics Chu, Shaoshuai Herty, Michael Kurganov, Alexander Lukacova-Medvidova, Maria Yu, Changsheng Numerical Analysis We study dissipative weak (DW) solutions of the Euler equations of gas dynamics using the first-, second-, third-, fifth-, seventh-, and ninth-order local characteristic decomposition-based central-upwind (LCDCU), low-dissipation central-upwind (LDCU), and viscous finite volume (VFV) methods, whose higher-order extensions are obtained via the framework of the alternative weighted essentially non-oscillatory (A-WENO) schemes. These methods are applied to several benchmark problems, including several two-dimensional Riemann problems and a Kelvin-Helmholtz instability test. The numerical results demonstrate that for methods converging only weakly in space and time, the limiting solutions are generalized DW solutions, approximated in the sense of ${\cal K}$-convergence and dependent on the numerical scheme. For all of the studied methods, we compute the associated Young measures and compare the DW solutions using entropy production and energy defect criteria. |
| title | Numerical Study of Dissipative Weak Solutions for the Euler Equations of Gas Dynamics |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2601.17452 |