Erratum: Kinetic analysis of thermally relativistic flow with dissipation [Phys. Rev. D83, 023517 (2011)]

Kinetic analysis of ultrarelativistic flow with dissipation

“…Before starting the discussion of ultrarelativistic flow with dissipation, we reconsider the mildly thermally relativistic flow with the small Lorentz contraction that was discussed in our previous studies [25,26] to investigate the effects of linearized Burnett terms on the dynamic pressure and heat flux from Eqs. (27) and (28).…”

“…However, we consider that our numerical analysis on the basis of the RBE may be useful for an initial understanding of the dissipation process of relativistic fluids with 1 . In our previous studies [25,26], the shock layer around the triangle prism generated by the supersonic rarefied flow with dissipation is analyzed under the small Lorentz contraction regime, ðuÞ 1:25, and the mildly thermally relativistic regime, 1 100, using the RBE and its kinetic models. In this paper, we numerically analyze the shock layer around the triangle prism generated by the supersonic rarefied flow using the RBE to investigate the dissipation process of relativistic fluids under the Lorentz contraction limit [1 ( ðuÞ] or the thermally relativistic limit ( < 1), where the RBE is solved for hard spherical partons using the direct simulation Monte Carlo (DSMC) method on the basis of our original algorithm [25].…”

“…In this paper, we numerically analyze the shock layer around the triangle prism generated by the supersonic rarefied flow using the RBE to investigate the dissipation process of relativistic fluids under the Lorentz contraction limit [1 ( ðuÞ] or the thermally relativistic limit ( < 1), where the RBE is solved for hard spherical partons using the direct simulation Monte Carlo (DSMC) method on the basis of our original algorithm [25]. Meanwhile, the simulation using the relativistic Boltzmann kinetic models, the Anderson-Witting [29] and modified Marle models [26], that was carried out in our previous study [26], is not conducted owing to the deficiency of the accuracy of the integration of the velocity distribution function under the ultrarelativistic limit. Here, we must remember that the shock layer problem is suitable to investigate the dissipation process of relativistic fluids, because the shock layer includes a strongly nonequilibrium regime such as the shock wave and thermal boundary layer, where the dissipation process of relativistic fluids is significant.…”

“…Bouras et al indicated that profiles of the pressure deviator and heat flux inside the shock wave obtained using the RBE are markedly different from those obtained using the Israel-Stewart equation, when the flow velocity driven by the shock wave is about 0:45c and the flow is rarefied. Recently, Yano et al [25,26] have numerically solved the shock layer around the triangle prism generated by the supersonic rarefied flow, using the RBE and its kinetic models as an initial study of the Mach cone problem [27,28] for mildly thermally relativistic matter, namely 1 100, where the triangle prism is a device to generate the steady shock wave and thermal boundary layer, which significantly depend on the dissipation process of the relativistic fluids. Yano et al indicated that thermally relativistic effects are significant, as well as the Lorentz contraction, to demonstrate the relativistic effects on the dissipation of relativistic fluids.…”

“…(23),(24),(26), and(27) using five variables (n, u i , and ), which are obtained (color online). Schematic of flow field when u 1 ¼ 0:999992c, 1 ¼ mc 2 =ðk 1 Þ ¼ 0:02, and w ¼ mc 2 =ðk w Þ ¼ 0:0003 (u 1 : flow velocity of the uniform flow, 1 : temperature of the uniform flow, w : temperature of the wall).…”