Kinetic analysis of ultrarelativistic flow with dissipation

Abstract

The ultrarelativistic shock layer around the triangle prism is numerically analyzed using the relativistic Boltzmann equation to investigate the dissipation process under two types of ultrarelativistic limits: namely, the Lorentz contraction limit, in which the uniform flow velocity approximates to the speed of light, and the thermally relativistic limit, in which the temperature of the uniform flow approximates to infinity. The relativistic Boltzmann equation is numerically solved using the direct simulation Monte Carlo method. We discuss dissipation process in the flow field by focusing on profiles of the dynamic pressure and heat flux along the stagnation streamline under the Lorentz contraction limit or the thermally relativistic limit. Our numerical results confirm that profiles of the dynamic pressure and heat flux along the stagnation streamline strongly depend on the Lorentz contraction and thermally relativistic effects under their ultrarelativistic limits, as predicted by Chapman-Enskog expansion on the basis of the generic Knudsen number.

Dissipation process of binary gas mixtures in thermally relativistic flow

“…In other words, the magnitude of the diffusion flux is sensitive to nonequilibrium terms beyond the NSF order approximation in the vicinity of the wall, although effects In above discussion on the diffusion flux, we postulated that the diffusion flux can be approximated using Chapman-Enskog approximation [32] [33], which also has been applied to the nonrelativistic mixture gas. On the other hand, we know that the diffusion flux does not depend on the generic Knudsen number [10] from Eq. (13).…”

“…( 13), we can readily understand that J α a is not a dissipating term, which depends on the generic Knudsen number, because N α a in Eq. (10) does not include dissipating terms, which depend on the generic Knudsen number.…”

“…For example, Bouras et al calculated the Riemann problem [7] or the Mach cone in the QGP jet [8] by calculating the RBE, whereas Yano et al [9] calculated the rarefied shock layer problem by calculating the RBE to investigate two types of relativistic effects, namely, thermally relativistic effect and Lorentz contraction effect, on dissipation process, where thermally relativistic matter is characterized using the thermally relativistic measure χ (χ = mc 2 /kθ: m: mass of a particle, c: speed of light, k: Boltzmann constant, θ: temperature) such as χ ≤ 100. In the author's previous studies [9] [10], the composition of thermally relativistic matter is limited to hard spherical particles with the equal mass and diameter, which never reflect the realistic collisional cross section of the QGP [1] [11]. Numerical results of dissipating terms such as the dynamic pressure and heat flux for the single component gas were compared with analytical results, which are obtained using the Navier-Stokes-Fourier (NSF) or Burnett order approximation [9] [10], where we applied transport coefficients for single component hard spherical particles such as the bulk viscosity, viscosity coefficient and thermal conductivity, which were calculated by Groot et al [12] or Cercignani and Kremer [13].…”

“…In the author's previous studies [9] [10], the composition of thermally relativistic matter is limited to hard spherical particles with the equal mass and diameter, which never reflect the realistic collisional cross section of the QGP [1] [11]. Numerical results of dissipating terms such as the dynamic pressure and heat flux for the single component gas were compared with analytical results, which are obtained using the Navier-Stokes-Fourier (NSF) or Burnett order approximation [9] [10], where we applied transport coefficients for single component hard spherical particles such as the bulk viscosity, viscosity coefficient and thermal conductivity, which were calculated by Groot et al [12] or Cercignani and Kremer [13].…”

“…Consequently, the diffusion flux was expressed with gradients of the five field variables (the density, flow velocity and temperature) [13] as a result of Chapman-Enskog method [17] or the first Maxwellian iteration of Grad's moment equations [22]. Indeed, the accurate diffusion flux must be calculated from the particle four flow by solving the RBE, which postulates the four velocity distinguished by each species of particles, because the diffusion flux is not a dissipating term, which depends on generic Knudsen number [10], unlike the dynamic pressure, pressure deviator and heat flux, when we define the diffusion flux using the four velocity distinguished by each species of particles.…”