The Taylor-von Neumann-Sedov blast-wave solution: comparisons with microscopic simulations of a one-dimensional gas
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arXiv
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| Format: | Preprint |
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2020
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| author | Ganapa, Santhosh Chakraborti, Subhadip Krapivsky, P. L. Dhar, Abhishek |
| author_facet | Ganapa, Santhosh Chakraborti, Subhadip Krapivsky, P. L. Dhar, Abhishek |
| contents | We study the response of an infinite system of point particles on the line initially at rest on the instantaneous release of energy in a localized region. We make a detailed comparison of the hydrodynamic variables predicted by Euler equations for non-dissipative ideal compressible gas and the results of direct microscopic simulations. At long times the profiles of the three conserved variables evolve to self-similar scaling forms, with a scaling exponent as predicted by the Taylor-von Neumann-Sedov (TvNS) blast-wave solution. The scaling functions obtained from the microscopic dynamics show a remarkable agreement with the TvNS predictions, except at the blast core, where the TvNS solution predicts a diverging temperature which is not observed in simulations. We show that the effect of heat conduction becomes important and present results from a numerical solution of the full Navier-Stokes-Fourier equations. A different scaling form is observed in the blast core and this is carefully analyzed. Our microscopic model is the one-dimensional alternate mass hard-particle gas which has the ideal gas equation of state but is non-integrable and known to display fast equilibration. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2010_15868 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The Taylor-von Neumann-Sedov blast-wave solution: comparisons with microscopic simulations of a one-dimensional gas Ganapa, Santhosh Chakraborti, Subhadip Krapivsky, P. L. Dhar, Abhishek Statistical Mechanics Computational Physics Fluid Dynamics We study the response of an infinite system of point particles on the line initially at rest on the instantaneous release of energy in a localized region. We make a detailed comparison of the hydrodynamic variables predicted by Euler equations for non-dissipative ideal compressible gas and the results of direct microscopic simulations. At long times the profiles of the three conserved variables evolve to self-similar scaling forms, with a scaling exponent as predicted by the Taylor-von Neumann-Sedov (TvNS) blast-wave solution. The scaling functions obtained from the microscopic dynamics show a remarkable agreement with the TvNS predictions, except at the blast core, where the TvNS solution predicts a diverging temperature which is not observed in simulations. We show that the effect of heat conduction becomes important and present results from a numerical solution of the full Navier-Stokes-Fourier equations. A different scaling form is observed in the blast core and this is carefully analyzed. Our microscopic model is the one-dimensional alternate mass hard-particle gas which has the ideal gas equation of state but is non-integrable and known to display fast equilibration. |
| title | The Taylor-von Neumann-Sedov blast-wave solution: comparisons with microscopic simulations of a one-dimensional gas |
| topic | Statistical Mechanics Computational Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2010.15868 |