Kinetic approach to relativistic dissipation

Abstract

Despite a long record of intense effort, the basic mechanisms by which dissipation emerges from the microscopic dynamics of a relativistic fluid still elude complete understanding. In particular, several details must still be finalized in the pathway from kinetic theory to hydrodynamics mainly in the derivation of the values of the transport coefficients. In this paper, we approach the problem by matching data from lattice-kinetic simulations with analytical predictions. Our numerical results provide neat evidence in favor of the Chapman-Enskog [The Mathematical Theory of Non-Uniform Gases, 3rd ed. (Cambridge University Press, Cambridge, U.K., 1970)] procedure as suggested by recent theoretical analyses along with qualitative hints at the basic reasons why the Chapman-Enskog expansion might be better suited than Grad's method [Commun. Pure Appl. Math. 2, 331 (1949)0010-364010.1002/cpa.3160020403] to capture the emergence of dissipative effects in relativistic fluids.

Relativistic lattice Boltzmann methods: Theory and applications

“…Another related application for RLBM is the theoretical study of relativistic transport coefficients. Based on RLBM simulations, recent works [45,47,48] have reported an accurate analysis of the relativistic transport coefficients in the single-relaxation time approximation, presenting numerical evidence that the Chapman Enskog expansion accurately relates kinetic transport coefficients and macroscopic hydrodynamic parameters in dissipative relativistic fluid dynamics, confirming recent theoretical results.…”

“…Indeed QGP in possibly the most natural field of application for RLBM methods. In this context it has been used to investigate several problems of shock waves propagation [18,36,[39][40][41][42][43][44][45] and other standard benchmarks, such as the 1-d Bjorken flow [37,43,46]. However, to the best of our knowledge, a fully-fledged implementation for simulating nuclear collisions has not been reported, as yet.…”

Relativistic dissipation obeys Chapman-Enskog asymptotics: Analytical and numerical evidence as a basis for accurate kinetic simulations

“…1a shows our new results for the nondimensional shear viscosity in (2 + 1) dimensions, while Fig. 1b shows results for the (3 + 1) dimensional case, previously presented in [35]. Our data clearly show that the Chapman-Enskog expansion correctly matches the measured behavior in all regimes, while this is not the case for Grad's method.…”

“…This question has been studied by several authors, at the theoretical level [11,19,22,[29][30][31][32][33], but only very recently has this extensive analysis -complemented by results of numerical simulations [14,25,34] -decidedly pointed in favour of the CE procedure; All these analyses are restricted to three-dimensional fluids in the ultrarelativistic limit, with virtually no results available in the arXiv:1901.08530v2 [nucl-th] 20 May 2019 mildly relativistic regime or for the two-dimensional case. A notable exception in (3 + 1) dimensions [35] shows that numerical simulations are able to clearly discriminate between CE and Grad's method on a wide range of kinematic regimes and neatly confirms that the CE approach is the correct one. While the (3+1)-dimensional case is obviously relevant in terms of potential applications, the study of relativistic fluids in lower dimensions may be of practical interest since it is considerably simpler to handle both at a mathematical [36] and computational level [37].…”

“…First, we consider shear viscosity; we follow [35] and consider as a benchmark the Taylor-Green vortex [65], a well known example of a decaying flow with an exact solution of the classic Navier-Stokes equations, and for which an approximate solution can be derived in the relativistic regime [35]. From the following initial conditions in a 2D periodic domain:…”