Fast kinetic simulator for relativistic matter.

Relativistic kinetic theory is ubiquitous to several fields of modern physics, finding application at large scales in systems in astrophysical contexts, all of the way down to subnuclear scales and into the realm of quark-gluon plasmas. This motivates the quest for powerful and efficient computational methods that are able to accurately study fluid dynamics in the relativistic regime as well as the transition to beyond hydrodynamics-in principle all of the way down to ballistic regimes. We present a family of relativistic lattice kinetic schemes for the efficient simulation of relativistic flows in both strongly (fluid) and weakly (rarefied gas) interacting regimes. The method can deal with both massless and massive particles, thereby encompassing ultra- and mildly relativistic regimes alike. The computational performance of the method for the simulation of relativistic flows across the aforementioned regimes is discussed in detail, along with prospects of future applications.

Probing bulk viscosity in relativistic flows.

We derive an analytical connection between kinetic relaxation rate and bulk viscosity of a relativistic fluid in d spatial dimensions, all the way from the ultra-relativistic down to the near non-relativistic regime. Our derivation is based on both Chapman-Enskog asymptotic expansion and Grad's method of moments. We validate our theoretical results against a benchmark flow, providing further evidence of the correctness of the Chapman-Enskog approach; we define the range of validity of this approach and provide evidence of mounting departures at increasing Knudsen number. Finally, we present numerical simulations of transport processes in quark-gluon plasmas, with special focus on the effects of bulk viscosity which might prove amenable to future experimental verification. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.

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

We present an analytical derivation of the transport coefficients of a relativistic gas in (2+1) dimensions for both Chapman-Enskog (CE) asymptotics and Grad's expansion methods. We further develop a systematic calibration method, connecting the relaxation time of relativistic kinetic theory to the transport parameters of the associated dissipative hydrodynamic equations. Comparison of our analytical results and numerical simulations shows that the CE method correctly captures dissipative effects, while Grad's method does not, in agreement with previous analyses performed in the (3+1)-dimensional case. These results provide a solid basis for accurately calibrated computational studies of relativistic dissipative flows.

Prospects for the Detection of Electronic Preturbulence in Graphene.

Based on extensive numerical simulations, accounting for electrostatic interactions and dissipative electron-phonon scattering, we propose experimentally realizable geometries capable of sustaining electronic preturbulence in graphene samples. In particular, preturbulence is predicted to occur at experimentally attainable values of the Reynolds number between 10 and 50, over a broad spectrum of frequencies between 10 and 100 GHz.

Kinetic approach to relativistic dissipation.

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.

Towards a unified lattice kinetic scheme for relativistic hydrodynamics.

We present a systematic derivation of relativistic lattice kinetic equations for finite-mass particles, reaching close to the zero-mass ultrarelativistic regime treated in the previous literature. Starting from an expansion of the Maxwell-Jüttner distribution on orthogonal polynomials, we perform a Gauss-type quadrature procedure and discretize the relativistic Boltzmann equation on space-filling Cartesian lattices. The model is validated through numerical comparison with standard tests and solvers in relativistic fluid dynamics such as Boltzmann approach multiparton scattering and previous relativistic lattice Boltzmann models. This work provides a significant step towards the formulation of a unified relativistic lattice kinetic scheme, covering both massive and near-massless particles regimes.