DIPLODOCUS I: Framework for the evaluation of relativistic transport equations with continuous forcing and discrete particle interactions

TL;DR

DIPLODOCUS introduces a new framework for modeling astrophysical systems by solving relativistic transport equations with a novel discretisation method that handles continuous forces and discrete particle interactions.

Contribution

It presents an analytical framework and discretisation scheme for relativistic transport equations, enabling accurate simulation of anisotropic interactions in astrophysical systems.

Findings

Developed an integral formulation of relativistic transport equations.

Created a conservative numerical scheme for particle distribution transport.

Validated the framework through initial test cases.

Abstract

DIPLODOCUS (Distribution-In-PLateaux methODOlogy for the CompUtation of transport equationS) is a novel framework being developed for the mesoscopic modelling of astrophysical systems via the transport of particle distribution functions through the seven dimensions of phase space, including continuous forces and discrete interactions between particles. This first paper in a series provides an overview of the analytical framework behind the model, consisting of an integral formulation of the relativistic transport equations (Boltzmann equations) and a discretisation procedure for the particle distribution function (Distribution-In-Plateaux). The latter allows for the evaluation of anisotropic interactions, and generates a conservative numerical scheme for a distribution function's transport through phase space.