Concentration and cavitation phenomena of Riemann solutions for the isentropic Euler system with the logarithmic equation of state
The analytical solutions of the Riemann problem for the isentropic Euler system with the logarithmic equation of state are derived explicitly for all the five different cases. The concentration and cavitation phenomena are observed and analyzed during the process of vanishing pressure in the Riemann...
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| Published in | Nonlinear analysis: real world applications Vol. 53; p. 103068 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier Ltd
01.06.2020
Elsevier BV |
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| Abstract | The analytical solutions of the Riemann problem for the isentropic Euler system with the logarithmic equation of state are derived explicitly for all the five different cases. The concentration and cavitation phenomena are observed and analyzed during the process of vanishing pressure in the Riemann solutions. It is shown that the solution consisting of two shock waves converges to a delta shock wave solution as well as the solution consisting of two rarefaction waves converges to a solution consisting of four contact discontinuities together with vacuum states with three different virtual velocities in the limiting situation. |
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| AbstractList | The analytical solutions of the Riemann problem for the isentropic Euler system with the logarithmic equation of state are derived explicitly for all the five different cases. The concentration and cavitation phenomena are observed and analyzed during the process of vanishing pressure in the Riemann solutions. It is shown that the solution consisting of two shock waves converges to a delta shock wave solution as well as the solution consisting of two rarefaction waves converges to a solution consisting of four contact discontinuities together with vacuum states with three different virtual velocities in the limiting situation. |
| ArticleNumber | 103068 |
| Author | Sun, Meina |
| Author_xml | – sequence: 1 givenname: Meina surname: Sun fullname: Sun, Meina email: smnwhy0350@163.com organization: School of Mathematics and Statistics Science, Ludong University, Yantai 264025, PR China |
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| Keywords | Logarithmic equation of state Delta shock wave Isentropic Euler system Riemann problem Vacuum state |
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| SubjectTerms | Cavitation Convergence Delta shock wave Equations of state Exact solutions Isentropic Euler system Logarithmic equation of state Rarefaction Riemann problem Shock waves Vacuum state |
| Title | Concentration and cavitation phenomena of Riemann solutions for the isentropic Euler system with the logarithmic equation of state |
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