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We present a numerical method for handling the resolution of a generaltransport equation for radiative particles, aimed at physical problems with ageneral spherical geometry. Having in mind the computational time difficultiesencountered in problems such as neutrino transport in astrophysical supernovae,we present a scheme based on full spectral methods in 6d spherical coordinates.This approach, known to be suited when the characteristic length of thedynamics is much smaller than the domain size, has the potential advantage of aglobal speedup with respect to usual finite difference schemes. An analysis ofthe properties of the Liouville operator expressed in our coordinates isnecessary in order to handle correctly the numerical behaviour of the solution.This reflects on a specific (spherical) geometry of the computational domain.The numerical tests, performed under several different regimes for theequation, prove the robustness of the scheme: their performances also point outto the suitability of such an approach to large scale computations involvingtransport physics for mass less radiative particles.

Solving the transport equation by the use of 6D spectral methods in spherical geometry