Numerical approximation of systems modeling large structure formation in cosmology

TL;DR

This paper introduces numerical methods for approximating two fluid dynamics systems that model large structure formation in cosmology, adapting the Godunov method for both nonrelativistic and relativistic fluids in an expanding universe.

Contribution

It develops a novel numerical approximation approach based on an extension of the Godunov method with delta wave projections, applicable to various cosmological fluid systems.

Findings

Effective numerical schemes for nonrelativistic and relativistic cosmological fluids.

Demonstrated stability and accuracy of the proposed methods.

Applicable to different fluid models in cosmology.

Abstract

Numerical approximations of two classical fluid dynamics systems modelling large structure formation in cosmology are proposed. These systems model nonrelativistic and relativistic fluids submitted to self-gravitation in an expanding background. They are obtained by an adaptation of an extension of the Godunov method, using delta wave projections, which was first introduced in Le Roux & al. for the system of pressureless fluid dynamics and which adapts to various systems of fluid dynamics.