We present a systematic account of recent developments of the relativistic Lattice Boltzmann method (RLBM) for dissipative hydrodynamics. We describe in full detail a unified, compact and dimension-independent procedure to design relativistic LB schemes capable of bridging the gap between the ultra-relativistic regime, k B T mc 2 , and the non-relativistic one, k B T mc 2 . We further develop a systematic derivation of the transport coefficients as a function of the kinetic relaxation time in d = 1, 2, 3 spatial dimensions. The latter step allows to establish a quantitative bridge between the parameters of the kinetic model and the macroscopic transport coefficients. This leads to accurate calibrations of simulation parameters and is also relevant at the theoretical level, as it provides neat numerical evidence of the correctness of the Chapman-Enskog procedure. We present an extended set of validation tests, in which simulation results based on the RLBMs are compared with existing analytic or semi-analytic results in the mildly-relativistic (k B T ∼ mc 2 ) regime for the case of shock propagations in quark-gluon plasmas and laminar electronic flows in ultra-clean graphene samples. It is hoped and expected that the material collected in this paper may allow the interested readers to reproduce the present results and generate new applications of the RLBM scheme.

We present a new method for the numerical solution of the radiative-transfer equation (RTE) in multidimensional scenarios commonly encountered in computational astrophysics. The method is based on the direct solution of the Boltzmann equation via an extension of the Lattice Boltzmann (LB) equation and allows to model the evolution of the radiation field as it interacts with a background fluid, via absorption, emission, and scattering. As a first application of this method, we restrict our attention to a frequency independent (“grey”) formulation within a special-relativistic framework, which can be employed also for classical computational astrophysics. For a number of standard tests that consider the performance of the method in optically thin, optically thick and intermediate regimes with a static fluid, we show the ability of the LB method to produce accurate and convergent results matching the analytic solutions. We also contrast the LB method with commonly employed moment-based schemes for the solution of the RTE, such as the M1 scheme. In this way, we are able to highlight that the LB method provides the correct solution for both non-trivial free-streaming scenarios and the intermediate optical-depth regime, for which the M1 method either fails or provides inaccurate solutions. When coupling to a dynamical fluid, on the other hand, we present the first self-consistent solution of the RTE with LB methods within a relativistic-hydrodynamic scenario. Finally, we show that besides providing more accurate results in all regimes, the LB method features smaller or comparable computational costs compared to the M1 scheme.

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.

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The rate of erosion of both ceramic and metal in a typical plasma jet igniter has been monitored as a function of various experimental parameters. Even under the most favorable conditions it appears that working lifetimes may be limited to the order of ten hours-a figure in line with previous measurements of arc erosion. Direct measurements of the thermal energy delivered by the igniter to the adjacent gas reveal that overall efficiencies approximately 10% are attained. In order to minimise erosion while maintaining a given delivery of thermal energy it is found essential to work with low initial voltages on the energy storage capacitor.

Measurements of the plasma efflux from a pulsed plasma jet igniter show that, contrary to previous expectations, plasma leaves the jet cavity in a substantially supersonic condition. Associated measurements of the electric field of the arc within the cavity and of the time taken for plasma to be expelled from the cavity show, together with the efflux measurements, good agreement with established arc theory and with a theory of plasma expansion based on a model in which the jet cavity is considered to act as the high-pressure section of a conventional shock tube. The implications of this model to the efficiency of a plasma igniter are discussed.

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