Non-linear Eulerian hydrodynamics of dark energy: Riemann problem and finite 
volume schemes

Blot, Linda; Corasaniti, Pier Stefano; Schmidt, Fabian

doi:10.1088/1475-7516/2023/05/001

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Non-linear Eulerian hydrodynamics of dark energy: Riemann problem and finite volume schemes

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Blot, Linda
Computational Structure Formation, MPI for Astrophysics, Max Planck Society;

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Schmidt, Fabian
Physical Cosmology, MPI for Astrophysics, Max Planck Society;

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Citation

Blot, L., Corasaniti, P. S., & Schmidt, F. (2023). Non-linear Eulerian hydrodynamics of dark energy: Riemann problem and finite volume schemes. Journal of Cosmology and Astroparticle Physics, 2023(5): 001. doi:10.1088/1475-7516/2023/05/001.

Cite as: https://hdl.handle.net/21.11116/0000-000D-E53D-D

Abstract

Upcoming large-scale structure surveys can shed new light on the properties of dark energy. In particular, if dark energy is a dynamical component, it must have spatial perturbations. Their behaviour is regulated by the speed of sound parameter, which is currently unconstrained. In this work, we present the numerical methods that will allow to perform cosmological simulations of inhomogeneous dark energy scenarios where the speed of sound is small and non-vanishing. We treat the dark energy component as an effective fluid and build upon established numerical methods for hydrodynamics to construct a numerical solution of the effective continuity and Euler equations. In particular, we develop conservative finite volume schemes that rely on the solution of the Riemann problem, which we provide here in both exact and approximate forms for the case of a dark energy fluid.