On conditions for weak conservativeness of regularized explicit finite-difference schemes for 1D barotropic gas dynamics equations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2018
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| _version_ | 1866909979208843264 |
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| author | Zlotnik, A. Lomonosov, T. |
| author_facet | Zlotnik, A. Lomonosov, T. |
| contents | We consider explicit two-level three-point in space finite-difference schemes for solving 1D barotropic gas dynamics equations. The schemes are based on special quasi-gasdynamic and quasi-hydrodynamic regularizations of the system. We linearize the schemes on a constant solution and derive the von Neumann type necessary condition and a CFL type criterion (necessary and sufficient condition) for weak conservativeness in $L^2$ for the corresponding initial-value problem on the whole line. The criterion is essentially narrower than the necessary condition and wider than a sufficient one obtained recently in a particular case; moreover, it corresponds most well to numerical results for the original gas dynamics system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1803_09899 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On conditions for weak conservativeness of regularized explicit finite-difference schemes for 1D barotropic gas dynamics equations Zlotnik, A. Lomonosov, T. Numerical Analysis We consider explicit two-level three-point in space finite-difference schemes for solving 1D barotropic gas dynamics equations. The schemes are based on special quasi-gasdynamic and quasi-hydrodynamic regularizations of the system. We linearize the schemes on a constant solution and derive the von Neumann type necessary condition and a CFL type criterion (necessary and sufficient condition) for weak conservativeness in $L^2$ for the corresponding initial-value problem on the whole line. The criterion is essentially narrower than the necessary condition and wider than a sufficient one obtained recently in a particular case; moreover, it corresponds most well to numerical results for the original gas dynamics system. |
| title | On conditions for weak conservativeness of regularized explicit finite-difference schemes for 1D barotropic gas dynamics equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/1803.09899 |