TY - JOUR
T1 - Conservative finite volume scheme for first-order viscous relativistic hydrodynamics
AU - Pandya, Alex
AU - Most, Elias R.
AU - Pretorius, Frans
N1 - Publisher Copyright:
© 2022 American Physical Society.
PY - 2022/6/15
Y1 - 2022/6/15
N2 - 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. The major difference between the two lies in the structure of the system of partial differential equations (PDEs): BDNK theory only has a set of conservation laws, whereas MIS also includes a set of evolution equations for its dissipative degrees of freedom. The simpler structure of the BDNK PDEs in this respect allows 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 multidimensional fluid solver for the BDNK equations suitable for physical applications. The scheme includes a flux-conservative discretization, nonoscillatory 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 and Pretorius [Phys. Rev. D 104, 023015 (2021)PRVDAQ2470-001010.1103/PhysRevD.104.023015].
AB - 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. The major difference between the two lies in the structure of the system of partial differential equations (PDEs): BDNK theory only has a set of conservation laws, whereas MIS also includes a set of evolution equations for its dissipative degrees of freedom. The simpler structure of the BDNK PDEs in this respect allows 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 multidimensional fluid solver for the BDNK equations suitable for physical applications. The scheme includes a flux-conservative discretization, nonoscillatory 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 and Pretorius [Phys. Rev. D 104, 023015 (2021)PRVDAQ2470-001010.1103/PhysRevD.104.023015].
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U2 - 10.1103/PhysRevD.105.123001
DO - 10.1103/PhysRevD.105.123001
M3 - Article
AN - SCOPUS:85132383088
SN - 2470-0010
VL - 105
JO - Physical Review D
JF - Physical Review D
IS - 12
M1 - 123001
ER -