Relativistic Hydrodynamics Research Articles

Evolutions in first-order viscous hydrodynamics

Motivated by the physics of the quark-gluon plasma created in heavy-ion collision experiments, we use holography to study the regime of applicability of various theories of relativistic viscous hydrodynamics. Using the microscopic description provided by holography of a system that relaxes to equilibrium, we obtain initial data with which we perform real-time evolutions in 2+1 dimensional conformal fluids using the first-order viscous relativistic hydrodynamics theory of Bemfica, Disconzi, Noronha and Kovtun (BDNK), BRSSS and ideal hydrodynamics. By initializing the hydrodynamics codes at different times, we can check the constitutive relations and assess the predictive power and accuracy of each of these theories.

Inverse-Reynolds-dominance approach to transient fluid dynamics

We consider the evolution equations for the bulk viscous pressure, diffusion current, and shear tensor derived within second-order relativistic dissipative hydrodynamics from kinetic theory. By matching the higher-order moments directly to the dissipative quantities, all terms which are of second order in the Knudsen number Kn vanish, leaving only terms of order $\mathcal{O}({\mathrm{Re}}^{\ensuremath{-}1}\mathrm{Kn})$ and $\mathcal{O}({\mathrm{Re}}^{\ensuremath{-}2})$ in the relaxation equations, where ${\mathrm{Re}}^{\ensuremath{-}1}$ is the inverse Reynolds number. We therefore refer to this scheme as the inverse-Reynolds-dominance (IReD) approach. The remaining (nonvanishing) transport coefficients can be obtained exclusively in terms of the inverse of the collision matrix. This procedure fixes unambiguously the relaxation times of the dissipative quantities, which are no longer related to the eigenvalues of the inverse of the collision matrix. In particular, we find that the relaxation times corresponding to higher-order moments grow as their order increases, thereby contradicting the separation of scales paradigm. The formal (up to second order) equivalence with the standard DNMR approach is proven and the connection between the IReD transport coefficients and the usual DNMR ones is established.

Bouncing cosmological model with general relativistic hydrodynamics in extended gravity

In this paper, in an extended theory of gravity, we have presented bouncing cosmological model at the backdrop of an isotropic, homogeneous space-time, in the presence of general relativistic hydrodynamics (GRH). The scale factor has been chosen in such a manner that with appropriate normalization, the quintom bouncing scenario can be assessed. Accordingly, the bounce occurs at [Formula: see text] and the corresponding Hubble parameter vanishes at the bounce epoch. The equation of state (EoS) parameter and the energy conditions of the model have been analyzed. The violation of strong energy condition further supports the behavior of extended gravity. As the bouncing cosmology suffers with instability, this model also shows the similar behavior.

Spin waves in spin hydrodynamics

The propagation properties of spin degrees of freedom are analyzed in the framework of relativistic hydrodynamics with spin based on the de Groot van Leeuwen--van Weert definitions of the energy-momentum and spin tensors. We derive the analytical expression for the spin wave velocity for arbitrary statistics and show that it goes to half the speed of light in the ultrarelativistic limit. We find that only the transverse degrees of freedom propagate, analogously to electromagnetic waves. Finally, we consider the effect of dissipative corrections and calculate the damping coefficients for the case of Maxwell-J\"uttner statistics.

On the structure of relativistic hydrodynamics for hot plasmas

Novel structure for the relativistic hydrodynamics of the classical plasmas is derived following the microscopic dynamics of the charged particles. The derivation is started from the microscopic definition of the concentration. Obviously, the concentration evolution leads to the continuity equation which gives the definition of the current of particles. Next, we consider the current evolution (it differs from the momentum density). It leads to novel functions which, to the best of our knowledge, have not been consider in the literature earlier. One of these functions is the average reverse relativistic gamma factor. Its current is also considered as one of basic functions. Evolution of new functions appears via the concentration and the particle current. So, the set of equations partially closes itself. Other functions are represented using the equations of state via the basic functions at the truncation procedure. The Langmuir waves are considered within the suggested model.

Λ spin polarization in event-by-event relativistic heavy-ion collisions

We present a systematic study of $\Lambda$ hyperon's polarization observables using event-by-event (3+1)D relativistic hydrodynamics. The effects of initial hot spot size and QGP's specific shear viscosity on the polarization observables are quantified. We examine the effects of the two formulations of the thermal shear tensor on the polarization observables using the same hydrodynamic background. With event-by-event simulations, we make predictions for the Fourier coefficients of $\Lambda$'s longitudinal polarization $P^z$ with respect to the event planes of different orders of anisotropic flow. We propose new correlations among the Fourier coefficients of $P^z$ and charged hadron anisotropic flow coefficients to further test the mapping from fluid velocity gradients to hyperon's polarization. Finally, we present a system size scan with Au+Au, Ru+Ru, and O+O collisions at $\sqrt{s_\mathrm{NN}} = 200$ GeV to study the system size dependence of polarization observables at the Relativistic Heavy-ion Collider.

Multicomponent second-order dissipative relativistic hydrodynamics with binary reactive collisions

We derive the multi-component second-order dissipative relativistic hydrodynamic equations using the moment-expansion method. By computing the transport coefficients using hard-sphere interactions, we investigate the role of multiple components and the reactive collisions. We find that both of these factors increase the effective cross-section and hence decrease the transport coefficients and relaxation times. We further compute such transport properties using leading-order perturbative QCD cross-sections. For both types of cross-sections, we find that the ratio between vector current relaxation time and conductivity for a multi-component fluid is notably different from that for a single-component fluid. Therefore, the current study provides a more applicable guideline for such a ratio in phenomenological hydrodynamics simulations.

Is first-order relativistic hydrodynamics in a general frame stable and causal for arbitrary interactions?

We derive a first-order, stable and causal, relativistic hydrodynamic theory from the microscopic kinetic equation using the gradient expansion technique in a general frame. The general frame is introduced from the arbitrary matching conditions for hydrodynamic fields. The interaction is introduced in the relativistic Boltzmann equation through the momentum-dependent relaxation time approximation (MDRTA) with the proposed collision operator that preserves the conservation laws. We demonstrate here for the first time that not only the general frame choice, but also the momentum dependence of microscopic interaction rate, captured through MDRTA, is imperative for producing the essential field corrections that give rise to a causal and stable first-order relativistic theory.

On the hydrodynamics of (2 + 1)-dimensional strongly coupled relativistic theories in an external magnetic field

In this paper, we review recent progress on relativistic hydrodynamics in (2 + 1) dimensions with an external magnetic field. We discuss the formalism allowing for momentum loss due to the explicit and spontaneous breaking of translation invariance by scalar operators. We also compare to some results from the gauge/gravity correspondence.

Impact of EMC effect on D meson modification factor in equilibrating QGP

In this article we employ the nuclear EMC effect to extract the parton distribution functions (PDFs) inside the Lead (Pb) and Gold (Au) nuclei. Extracted PDFs are utilized to obtain the transverse momentum dependent (TMD) ones, using the computing codes like Pythia 8 or MCFM-10. Through this procedure TMDPDFs for charm and bottom quarks in Au at $\sqrt{s_{NN}}=200\;GeV$, Pb at $\sqrt{s_{NN}}=2.76\;TeV$ and $\sqrt{s_{NN}}=5.02\;TeV$ are calculated. To evaluate the validity of results and investigate the influence of nuclear EMC effect, the numerated TMDs are used as input to estimate heavy quark modification factor $R_{AA}$ at transverse plane $P_T$. This observable is calculated through numerical solution of the Fokker-Planck equation. For this purpose we need to extract the drag and diffusion coefficients, using the hard thermal loop correction. It is done in the frame work of the relativistic hydrodynamics up to the third order approximation of gradient expansion. The results are compared with same solutions when the input PFDs are considered inside the unbounded protons where the nuclear effect is not included. The comparison indicates a significant improvement of computed $R_{AA}$ with available experimental data when the EMC effect is considered.

Pseudogauges and relativistic spin hydrodynamics for interacting Dirac and Proca fields

We present the explicit expressions of different pseudo-gauge transformations for Dirac and Proca fields considering a general interaction term. The particular case of the interaction of Dirac and Proca fields with a background electromagnetic field is also studied. Starting from the quantum kinetic theory with collisions derived from the Wigner-function formalism for massive spin-1/2 and spin-1 particles, we establish a connection between different pseudo-gauges and relativistic spin hydrodynamics. The physical implications of the various decompositions of orbital and spin angular momentum are discussed.

Analytic solutions of relativistic dissipative spin hydrodynamics with radial expansion in Gubser flow

We have derived the analytic solutions of dissipative relativistic spin hydrodynamics with Gubser expansion. Following the standard strategy of deriving the solutions in a Gubser flow, we take the Weyl rescaling and obtain the energy-momentum and angular momentum conversation equations in the $dS_{3}\times\mathbb{R}$ space-time. We then derive the analytic solutions of spin density, spin potential and other thermodynamic in $dS_{3}\times\mathbb{R}$ space-time and transform them back into Minkowski space-time $\mathbb{R}^{3,1}$. In the Minkowski space-time, the spin density and spin potential including the information of radial expansion decay as $\sim L^{-2}\tau^{-1}$ and $\sim L^{-2}\tau^{-1/3}$ in large $L$ limit, with $\tau$ being proper time and $L$ being the characteristic length of the system, respectively. Moreover, we observe the non-vanishing spin corrections to the energy density and other dissipative terms in the Belinfante form of dissipative spin hydrodynamics. Our results can also be used as test beds for future simulations of relativistic dissipative spin hydrodynamics.

On high-order numerical schemes for viscous relativistic hydrodynamics through the Kelvin–Helmholtz instability

ABSTRACT This work assesses the dissipative properties of high-order numerical methods for relativistic hydrodynamics. A causal theory of physical dissipation is included within a finite volume high-resolution shock-capturing framework based on the Israel–Stewart theory to study high-order WENO (weighted-essentially non-oscillatory) schemes for simulating the relativistic Kelvin–Helmholtz instability. We provide an estimation of the numerical dissipation of high-order schemes based on results obtained both with and without physically resolved dissipation and determine an empirical relationship between the numerical dissipation and the grid resolution. We consider the appearance of secondary flow features within the evolution of the Kelvin–Helmholtz instability and determine that they are numerical artifacts — this is partly based on arguments presented in terms of a frame-dependent form of the relativistic Reynolds number. There is a potential advantage of using high-order schemes in terms of their accuracy and computational cost on coarser grid resolutions when directly compared to low-order schemes on a fine grid in the presence of physical viscosity. It is possible to find reasonable agreement between numerical results that employ lower-order schemes using a finer grid resolution and results that employ higher order schemes at a coarser grid resolution when sufficient viscosity is present. Overall, the present analysis gives an insight into the numerical dissipation of high-order shock-wave capturing schemes which can be relevant to computational studies of astrophysical phenomena in the relativistic regime. The results presented herein are problem and scheme-dependent and serve to highlight the different roles of numerical and physical dissipation.

Transient Relativistic Fluid Dynamics in a General Hydrodynamic Frame.

We propose a new theory of second-order viscous relativistic hydrodynamics which does not impose any frame conditions on the choice of the hydrodynamic variables. It differs from Mueller-Israel-Stewart theory by including additional transient degrees of freedom, and its first-order truncation reduces to Bemfica-Disconzi-Noronha-Kovtun theory. Conditions for causality and stability are explicitly given in the conformal regime. As an illustrative example, we consider Bjorken flow solutions to our equations and identify variables which make a hydrodynamic attractor manifest.

A physical-constraint-preserving finite volume WENO method for special relativistic hydrodynamics on unstructured meshes

This paper presents a highly robust third-order accurate finite volume weighted essentially non-oscillatory (WENO) method for special relativistic hydrodynamics on unstructured triangular meshes. We rigorously prove that the proposed method is physical-constraint-preserving (PCP), namely, always preserves the positivity of the pressure and the rest-mass density as well as the subluminal constraint on the fluid velocity. The method is built on a highly efficient compact WENO reconstruction on unstructured meshes, a simple PCP limiter, the provably PCP property of the Harten–Lax–van Leer flux, and third-order strong-stability-preserving time discretization. Due to the relativistic effects, the primitive variables (namely, the rest-mass density, velocity, and pressure) are highly nonlinear implicit functions in terms of the conservative variables, making the design and analysis of our method nontrivial. To address the difficulties arising from the strong nonlinearity, we adopt a novel quasilinear technique for the theoretical proof of the PCP property. Three provable convergence-guaranteed iterative algorithms are also introduced for the robust recovery of primitive quantities from admissible conservative variables. We also propose a slight modification to an existing WENO reconstruction to ensure the scaling invariance of the nonlinear weights and thus to accommodate the homogeneity of the evolution operator, leading to the advantages of the modified WENO reconstruction in resolving multi-scale wave structures. Extensive numerical examples are presented to demonstrate the robustness, expected accuracy, and high resolution of the proposed method.

Explosion of a Minimum-Mass Neutron Star within Relativistic Hydrodynamics

The relativistic hydrodynamics equations are adapted for the spherically symmetric case and the Lagrangian form. They are used to model the explosive disruption of a minimum-mass neutron star: a key ingredient of the stripping model for short gamma-ray bursts. The shock breakout from the neutron star surface accompanied by the acceleration of matter to ultrarelativistic velocities is studied. A comparison with the results of previously published nonrelativistic calculations is made.

Conservative finite volume scheme for first-order viscous relativistic hydrodynamics

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 M\"uller-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)].

A New Parallel Code Based on a Simple Piecewise Parabolic Method for Numerical Modeling of Colliding Flows in Relativistic Hydrodynamics

A new parallel code based on models of special relativistic hydrodynamics is presented for describing interacting flows. A new highly accurate numerical method is considered and verified. A parallel implementation of the method by means of Coarray Fortran technology and its efficiency are described in detail. The code scalability is 92% on a cluster with Intel Xeon 6248R NKS-1P with 192 Coarray Fortran images. Different interacting relativistic flows are considered as astrophysical applications.

Spin polarization formula for Dirac fermions at local equilibrium

We derive a Cooper-Frye type spin polarization formula for Dirac fermions at local thermal equilibrium described by a grand canonical ensemble specified by temperature, fluid velocity, chemical potential, and spin potential. We discuss the physical meaning of different contributions to spin polarization and compare them with previous works. The present formula provides machinery to convert the spin potential computed in, e.g., relativistic spin hydrodynamics to the spin polarization observable in, e.g., heavy-ion collisions.

Extended relaxation time approximation and relativistic dissipative hydrodynamics

Development of a new framework for derivation of order-by-order hydrodynamics from Boltzmann equation is necessary as the widely used Anderson-Witting formalism leads to violation of fundamental conservation laws when the relaxation-time depends on particle energy, or in a hydrodynamic frame other than the Landau frame. We generalize an existing framework for consistent derivation of relativistic dissipative hydrodynamics from the Boltzmann equation with an energy-dependent relaxation-time by extending the Anderson-Witting relaxation-time approximation. We argue that the present framework is compatible with conservation laws and derive first-order hydrodynamic equations in landau frame. Further, we show that the transport coefficients, such as shear and bulk viscosity as well as charge and heat diffusion currents, have corrections due to the energy dependence of relaxation-time compared to what one obtains from the Anderson-Witting approximation of the collision term. The ratios of these transport coefficients are studied using a parametrized relaxation-time, and several interesting scaling features are reported.