Stability and causality in relativistic dissipative hydrodynamics

Denicol, Gabriel S.; Kodama, T.; Koide, T.; Mota, Ph.

doi:10.1088/0954-3899/35/11/115102

Cited by 157 publications

(260 citation statements)

References 35 publications

(58 reference statements)

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“…The study of the short wavelength limit is surely limited to phenomenological applications of fluid dynamics; however, since the relativistic Navier-Stokes theory is known to have numerical instabilities, we find it useful to check that the Israel-Stewart construction is free of any acausality and instability in this regime under linear perturbations. Our results from this section are consistent with the discussion presented in [27,28].…”

Section: Stability and Causalitysupporting

confidence: 92%

Nonlinear waves in second order conformal hydrodynamics

et al. 2015

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In this work we study wave propagation in dissipative relativistic fluids described by a simplified set of the 2nd order viscous conformal hydrodynamic equations corresponding to Israel-Stewart theory. Small amplitude waves are studied within the linearization approximation while waves with large amplitude are investigated using the reductive perturbation method, which is generalized to the case of 2nd order relativistic hydrodynamics. Our results indicate the presence of a "soliton-like" wave solution in Israel-Stewart hydrodynamics despite the presence of dissipation and relaxation effects.

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Section: Stability and Causalitysupporting

confidence: 92%

Nonlinear waves in second order conformal hydrodynamics

et al. 2015

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“…In this work we will neglect such terms and use instead the relaxation-type equation given in Eq. (12), that is obtained from a second-order gradient expansion.…”

Section: A Transport Coefficients and The Speed Of Soundmentioning

confidence: 99%

“…The impact of the temperature dependence of transport coefficients on momentum anisotropies that are obtained from hydrodynamic models was recently investigated in Refs. [8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Dissipative hydrodynamics coupled to chiral fields

Peralta-Ramos

Krein

2011

Phys. Rev. C

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Using second-order dissipative hydrodynamics coupled self-consistently to the linear σ model we study the 2 + 1 dimensional evolution of the fireball created in Au+Au relativistic collisions. We analyze the influence of the dynamics of the chiral fields on the charged-hadron elliptic flow v 2 and on the ratio v 4 /(v 2 ) 2 for a temperature-independent as well as for a temperature-dependent viscosity-to-entropy ratio η/s calculated from the linearized Boltzmann equation in the relaxation time approximation. We find that v 2 is not very sensitive to the coupling of chiral sources to the hydrodynamic evolution, but the temperature dependence of η/s plays a much bigger role on this observable. On the other hand, the ratio v 4 /(v 2 ) 2 turns out to be much more sensitive than v 2 to both the coupling of the chiral sources and the temperature dependence of η/s.

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“…Another important mechanism is the finiteness of fluid cells to be applied thermodynamic relations [6]. In the derivation of hydrodynamics, it is assumed that the local equilibrium is achieved in each fluid cells which has finite spatial extension (to be rigorous, it should be infinite compared with the microscopic scale).…”

Section: Memory Effects On Extensive Measuresmentioning

confidence: 99%

“…In such extreme situation, we can analytically show that the mass matrix associated with the simple causal dissipative hydrodynamics Eq. (9) becomes negative, hence it is unstable [6].…”

Section: Memory Effects On Extensive Measuresmentioning

confidence: 99%

Memory effects and transport coefficients for non-Newtonian fluids

Kodama¹,

Koide²

2009

J. Phys. G: Nucl. Part. Phys.

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Abstract. We discuss the roles of viscosity in relativistic fluid dynamics from the point of view of memory effects. Depending on the type of quantity to which the memory effect is applied, different terms appear in higher order corrections. We show that when the memory effect applies on the extensive quantities, the hydrodynamic equations of motion become non-singular. We further discuss the question of memory effect in the derivation of transport coefficients from a microscopic theory. We generalize the application of the Green-Kubo-Nakano (GKN) to calculate transport coefficients in the framework of projection operator formalism, and derive the general formula when the fluid is non-Newtonian. Non-Newtonian Nature of a Dissipative Fluid in Relativistic RegimeThe effect of dissipation in relativistic fluids is one of current topics in the physics of relativistic heavy-ion collisions [1]. Here, we discuss this problem focusing on the memory effect on irreversible current. It is well-known that in a simple covariant extension of the Navier-Stokes theory there appears the problem of relativistic acausality and instability associated with it. First let us illustrate using the example of diffusion equation, the basic idea of memory effect as the solution for the problem of acausality in relativistic hydrodynamics.In the usual derivation of diffusion equation, we assume that the irreversible current J(t) is simply proportional to the corresponding thermodynamic force F (t),where D is a transport coefficient. The fluid whose irreversible current posseses this property is referred to as a Newtonian fluid, and the evolution is described by, for example, the Navier-Stokes equation. However, to be exact, there should exist some time retardation effect in generating the current in the medium, when a thermodynamic force is applied (remember the linear response theory). The expression (1) is justified only when there is clear separation of microscopic and macroscopic scales and the retardation effect is negligible. This assumption is usually satisfied in fluid around us, where the

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Stability and causality in relativistic dissipative hydrodynamics

Cited by 157 publications

References 35 publications

Nonlinear waves in second order conformal hydrodynamics

Nonlinear waves in second order conformal hydrodynamics

Dissipative hydrodynamics coupled to chiral fields

Memory effects and transport coefficients for non-Newtonian fluids

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