We present a systematic procedure for the construction of relativistic lattice Boltzmann models (R-SLB) appropriate for the simulation of flows of massless particles. Quadrature rules are used for the discretization of the momentum space in spherical coordinates. The models are optimized for one-dimensional flows. The applications considered in this paper are the Sod shock tube and the one-dimensional boost invariant expansion (Bjorken flow). Our models are tested against exact solutions in the inviscid and ballistic limits. At intermediate relaxation times (finite viscosity), we compare with the results obtained using the Boltzmann approach of multiparton scattering model for the Sod shock tube problem, as well as with a semianalytic solution for the nonideal Bjorken flow. In all cases our models give remarkably good results. We define a convergence test in order to find the quadrature order necessary to obtain convergence at a predefined accuracy. We show that, while in the hydrodynamic regime the number of velocities is comparable to that required for the more popular collision-streaming type models, as we go towards the ballistic regime, the size of the velocity set must be substantially increased in order to accurately reproduce the analytic profiles.

We consider an application of the tetrad formalism introduced by Cardall et al. [Phys. Rev. D 88 (2013) 023011] to the problem of a rigidly rotating relativistic gas in thermal equilibrium and discuss the possible applications of this formalism to rel- ativistic lattice Boltzmann simulations. We present in detail the transformation to the comoving frame, the choice of tetrad, as well as the explicit calculation and analysis of the components of the equilibrium particle ow four-vector and of the equilibrium stress-energy tensor.

In this paper, a procedure for generating a family of parametrical broadband clear-sky models is described. The key element is the conversion of one or more model input variables into tunable mathematical parameters. The approach is tested on the PS model [Paulescu, M. and Schlett, Z., Theor. Appl. Climatol. 75, 203 (2003)], with the free parameter being the Ångström exponent (α). This allows us to fine-tune for conditions dominated by desert dust, urban-industrial, and mixed aerosols. We find that for an arbitrary set of data, the optimal value of the free parameter is not the same as its actual measured value (inserting the measured value in the model would result in a lower performance). We attribute this fact to the inaccurate nature of the base model. The optimal α value varies with the considered solar irradiance component, aerosol type and loading, and the error measure(s) used for assessing model accuracy. A set of recommended models for each aerosol type and loading class is given. The tabled values for the aerosol transmittance coefficients are also listed. A preliminary validation shows that the newly developed models are very reliable. The optimal version generally falls within a few percent of the results of REST2v5, a benchmark model in clear-sky solar irradiance estimation. While some established models outperform REST2v5 for certain aerosol types and for only one solar irradiance component, the new models prove competitive under most scenarios. Beyond showing the performance of the developed model family, these results hint at great potential of our approach.