Numerical study of loss of hyperbolicity using a cold plasma model
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arXiv
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| Natura: | Preprint |
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2026
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| _version_ | 1866910010907295744 |
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| author | Chizhonkov, Evgeniy V. Rozanova, Olga S. |
| author_facet | Chizhonkov, Evgeniy V. Rozanova, Olga S. |
| contents | We study a one-dimensional system of cold plasma equations taking into account electron-ion collisions in both relativistic and nonrelativistic cases. It is known that for a constant collision coefficient $ν$, the solution to the Cauchy problem for such a system can lose smoothness. However, if the dependence of $ν$ on the electron density $N$ is more than linear, then the solution remains globally smooth for any initial data. However, the appearance of the dependence $ν(N)$ leads to a change in the type of the system, it loses hyperbolicity, which leads to computational problems. In this paper, we propose a new implicit solution method in Euler variables that overcomes these difficulties. It can be used in both nonrelativistic and relativistic cases and is tested for the threshold case of a linear dependence $ν(N)=ν_1+ν_0 N$, when smoothness can still be lost. The computational experiments carried out are in full agreement with the available theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03859 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Numerical study of loss of hyperbolicity using a cold plasma model Chizhonkov, Evgeniy V. Rozanova, Olga S. Computational Physics Numerical Analysis Plasma Physics 65M06, 65M22, 65H10, 65Z05, 82D10 We study a one-dimensional system of cold plasma equations taking into account electron-ion collisions in both relativistic and nonrelativistic cases. It is known that for a constant collision coefficient $ν$, the solution to the Cauchy problem for such a system can lose smoothness. However, if the dependence of $ν$ on the electron density $N$ is more than linear, then the solution remains globally smooth for any initial data. However, the appearance of the dependence $ν(N)$ leads to a change in the type of the system, it loses hyperbolicity, which leads to computational problems. In this paper, we propose a new implicit solution method in Euler variables that overcomes these difficulties. It can be used in both nonrelativistic and relativistic cases and is tested for the threshold case of a linear dependence $ν(N)=ν_1+ν_0 N$, when smoothness can still be lost. The computational experiments carried out are in full agreement with the available theoretical results. |
| title | Numerical study of loss of hyperbolicity using a cold plasma model |
| topic | Computational Physics Numerical Analysis Plasma Physics 65M06, 65M22, 65H10, 65Z05, 82D10 |
| url | https://arxiv.org/abs/2602.03859 |