Use of the lattice Boltzmann method (LBM) has been extended to analyze radiative transport problems in an absorbing, emitting, and scattering medium. In terms of collision and streaming, the present approach of the LBM for radiative heat transfer is similar to those being used in fluid dynamics and heat transfer for the analyses of conduction and convection problems. However, to mitigate the effect of the isotropy in the polar direction, in the present LBM approach, lattices with more number of directions than those being used for the 2-D system have been employed. The LBM formulation has been validated by solving benchmark radiative equilibrium problems in 1-D and 2-D Cartesian geometry. Temperature and heat flux distributions have been obtained for a wide range of extinction coefficients. The LBM results have been compared against the results obtained from the finite-volume method (FVM). Good comparison has been obtained. The numbers of iterations and CPU times for the LBM and the FVM have also been compared. The number of iterations in the LBM has been found to be much more than the FVM. However, computationally, the LBM has been found to be much faster than the FVM.

The present work introduces an empirically ground agent-based modeling (ABM) framework to assess the spatial and temporal diffusion of rooftop photovoltaic (PV) systems on existing buildings of a city district. The overall ABM framework takes into account social, technical, environmental and economic aspects to evaluate the diffusion of PV technology in the urban context. A city district that includes 18,720 households distributed over 1,290 building blocks and a surface area of 2.47 square kilometers is used to test the proposed ABM framework. Results show how the underlying regulatory framework (i.e., the rules of the internal electricity market) influences the pattern and intensity of adoption, thus realizing different shares of the available potential. Policies that support the establishment of ’prosumers’ within Condominiums (i.e., energy community buildings), and not in single-family houses only, is key to yield high diffusion rates. The installed capacity increases by 80% by switching from the one-to-one configuration to the one-to-many paradigm, i.e., from 5.90 MW of rooftop PV installed on single-family households and/or single PV owners to 10.64 MW in energy community buildings. Moreover, the possibility to spread the auto-generated solar electricity over the load profile of the entire population of a Condominium results in self-consumption rates greater than 50% and self-sufficiency ratios above 20% for the majority of the simulated buildings.