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

TL;DR

This paper introduces a 6D spectral method for solving the transport equation in spherical geometry, aiming to improve computational efficiency in astrophysical problems like neutrino transport.

Contribution

The paper presents a novel 6D spectral numerical scheme tailored for spherical geometries, enhancing speed and robustness over traditional finite difference methods.

Findings

The spectral method is robust across various regimes.

It offers potential global speedup in large-scale transport simulations.

The approach is suitable for massless radiative particle transport.

Abstract

We present a numerical method for handling the resolution of a general transport equation for radiative particles, aimed at physical problems with a general spherical geometry. Having in mind the computational time difficulties encountered 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 the dynamics is much smaller than the domain size, has the potential advantage of a global speedup with respect to usual finite difference schemes. An analysis of the properties of the Liouville operator expressed in our coordinates is necessary 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 the equation, prove the robustness of the scheme: their performances also point out to the suitability of such an approach to large scale computations involving transport physics for mass less radiative particles.