Radiative transfer for variable three-dimensional atmospheres

To study the temperature in a gas subjected to electromagnetic radiations, one may use the Radiative Transfer equations coupled with the Navier-Stokes equations. The problem has 7 dimensions; however with minimal simplifications it is equivalent to a small number of integro-differential equations in 3 dimensions. We present the method and a numerical implementation using an H-matrix compression scheme. The result is very fast: 240K physical points, all directions of radiation and 683 frequencies require less than 35 minutes on an Apple M1 Laptop. The method is capable of handling variable absorption and scattering functions of spatial positions and frequencies.