Conservative finite volume scheme for first-order viscous relativistic hydrodynamics

Abstract

We present the first conservative finite volume numerical scheme for the causal, stable relativistic Navier-Stokes equations developed by Bemfica, Disconzi, Noronha, and Kovtun (BDNK). BDNK theory has arisen very recently as a promising means of incorporating entropy-generating effects (viscosity, heat conduction) into relativistic fluid models, appearing as a possible alternative to the so-called Müller-Israel-Stewart (MIS) theory successfully used to model quark-gluon plasma. Both BDNK and MIS-type theories may be understood in terms of a gradient expansion about the perfect (ideal) fluid, wherein BDNK arises at first order and MIS at second order. As such, BDNK has vastly fewer terms and undetermined model coefficients (as is typical for an effective field theory appearing at lower order), allowing for rigorous proofs of stability, causality, and hyperbolicity in full generality which have as yet been impossible for MIS. To capitalize on these advantages, we present the first fully conservative multi-dimensional fluid solver for the BDNK equations suitable for physical applications. The scheme includes a flux-conservative discretization, non-oscillatory reconstruction, and a central-upwind numerical flux, and is designed to smoothly transition to a high-resolution shock-capturing perfect fluid solver in the inviscid limit. We assess the robustness of our new method in a series of flat-spacetime tests for a conformal fluid, and provide a detailed comparison with previous approaches of Pandya & Pretorius (2021) [1].

Perturbative approaches in relativistic kinetic theory and the emergence of first-order hydrodynamics

“…Once again, since the linearized collision term L is a linear operator, the particular solution φ part p must have the general form (42),…”

“…This framework has also been explored numerically in Refs. [40][41][42], where it was compared to other hydrodynamic formulations.…”