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On the Nature of Turbulence
, 1971
"... A mechanism for the generation of turbulence and related phenomena in dissipative systems is proposed. ..."
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Cited by 233 (4 self)
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A mechanism for the generation of turbulence and related phenomena in dissipative systems is proposed.
A Boundary Condition Capturing Method for Multiphase Incompressible Flow
 J. Sci. Comput
, 2000
"... In [6], the Ghost Fluid Method (GFM) was developed to capture the boundary conditions at a contact discontinuity in the inviscid compressible Euler equations. In [11], related techniques were used to develop a boundary condition capturing approach for the variable coefficient Poisson equation on dom ..."
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Cited by 138 (25 self)
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In [6], the Ghost Fluid Method (GFM) was developed to capture the boundary conditions at a contact discontinuity in the inviscid compressible Euler equations. In [11], related techniques were used to develop a boundary condition capturing approach for the variable coefficient Poisson equation on domains with an embedded interface. In this paper, these new numerical techniques are extended to treat multiphase incompressible flow including the effects of viscosity, surface tension and gravity. While the most notable finite difference techniques for multiphase incompressible flow involve numerical smearing of the equations near the interface, see e.g. [19, 17, 1], this new approach treats the interface in a sharp fashion. We would like to thank Dr. David Wasson of Arete Entertainment (www.areteis.com) for developing the fast level set rendering software that was used in the visualization of the three dimensional calculations.
Electroweak baryon number nonconservation in the early universe and in highenergy collisions,”Uspekhi
 Fizicheskikh Nauk,
, 1996
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Quasiincompressible Cahn–Hilliard fluids and topological transitions
 Proc. R. Soc. Lond. A
, 1998
"... One of the fundamental problems in simulating the motion of sharp interfaces between immiscible fluids is a description of the transition that occurs when the interfaces merge and reconnect. It is well known that classical methods involving sharp interfaces fail to describe this type of phenomena. F ..."
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Cited by 100 (4 self)
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One of the fundamental problems in simulating the motion of sharp interfaces between immiscible fluids is a description of the transition that occurs when the interfaces merge and reconnect. It is well known that classical methods involving sharp interfaces fail to describe this type of phenomena. Following some previous work in this area, we suggest a physically motivated regularization of the Euler equations which allows topological transitions to occur smoothly. In this model, the sharp interface is replaced by a narrow transition layer across which the fluids may mix. The model describes a flow of a binary mixture, and the internal structure of the interface is determined by both diffusion and motion. An advantage of our regularization is that it automatically yields a continuous description of surface tension, which can play an important role in topological transitions. An additional scalar field is introduced to describe the concentration of one of the fluid components and the resulting system of equations couples the Euler (or Navier–Stokes) and the Cahn–Hilliard equations. The model takes into account weak nonlocality (dispersion) associated with an internal length scale and localized dissipation due
Hydrodynamic description of ultrarelativistic heavyion collisions
, 2003
"... Relativistic hydrodynamics has been extensively applied to high energy heavyion collisions. We review hydrodynamic calculations for Au+Au collisions at RHIC energies and provide a comprehensive comparison between the model and experimental data. The model provides a very good description of all mea ..."
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Cited by 77 (3 self)
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Relativistic hydrodynamics has been extensively applied to high energy heavyion collisions. We review hydrodynamic calculations for Au+Au collisions at RHIC energies and provide a comprehensive comparison between the model and experimental data. The model provides a very good description of all measured momentum distributions in central and semiperipheral Au+Au collisions, including the momentum anisotropies (elliptic flow) and systematic dependencies on the hadron rest masses up to transverse momenta of about 1.5–2 GeV/c. This provides impressive evidence that the bulk of the fireball matter shows efficient thermalization and behaves hydrodynamically. At higher pT the hydrodynamic model begins to gradually break down, following an interesting pattern which we discuss. The elliptic flow anisotropy is shown to develop early in the collision and to provide important information about the early expansion stage, pointing to the formation of a highly equilibrated quarkgluon plasma at energy densities well above the deconfinement threshold. Twoparticle momentum correlations provide information about the spatial structure of the fireball (size, deformation, flow) at the end of the collision. Hydrodynamic calculations of the twoparticle correlation functions do not describe the data very well. Possible origins of the discrepancies are discussed but not fully resolved, and further measurements to help clarify this situation are suggested.
Fluid dynamics of Rcharged black holes
"... We construct electrically charged AdS5 black hole solutions whose charge, mass and boostparameters vary slowly with the spacetime coordinates. From the perspective of the dual theory, these are equivalent to hydrodynamic configurations with varying chemical potential, temperature and velocity fiel ..."
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Cited by 75 (3 self)
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We construct electrically charged AdS5 black hole solutions whose charge, mass and boostparameters vary slowly with the spacetime coordinates. From the perspective of the dual theory, these are equivalent to hydrodynamic configurations with varying chemical potential, temperature and velocity fields. We compute the boundary theory transport coefficients associated with a derivative expansion of the energy momentum tensor and Rcharge current up to second order. In particular, we find a first order transport coefficient
A FrontTracking Algorithm for Accurate Representation of Surface Tension
, 1999
"... We present a front tracking algorithm for the solution of the 2D incompressible NavierStokes equations with interfaces and surface forces. More particularly, we focus our attention on the accurate description of the surface tension terms and the associated pressure jump. We consider the stationary ..."
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Cited by 73 (9 self)
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We present a front tracking algorithm for the solution of the 2D incompressible NavierStokes equations with interfaces and surface forces. More particularly, we focus our attention on the accurate description of the surface tension terms and the associated pressure jump. We consider the stationary Laplace solution for a bubble with surface tension. A careful treatment of the pressure gradient terms at the interface allows us to reduce the spurious currents to the machine precision. Good results are obtained for the oscillation of a capillary wave compared with the linear viscous theory. A classical test of RayleighTaylor instability is presented.
Numerical Methods For Hyperbolic Conservation Laws With Stiff Relaxation I. Spurious Solutions
 SIAM J. Sci. Comput
, 1992
"... . We consider the numerical solution of hyperbolic systems of conservation laws with relaxation using a shock capturing finite difference scheme on a fixed, uniform spatial grid. We conjecture that certain a priori criteria insure that the numerical method does not produce spurious solutions as the ..."
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Cited by 73 (2 self)
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. We consider the numerical solution of hyperbolic systems of conservation laws with relaxation using a shock capturing finite difference scheme on a fixed, uniform spatial grid. We conjecture that certain a priori criteria insure that the numerical method does not produce spurious solutions as the relaxation time vanishes. One criterion is that the limits of vanishing relaxation time and vanishing viscosity commute for the viscous regularization of the hyperbolic system. A second criterion is that a certain "subcharacteristic" condition be satisfied by the hyperbolic system. We support our conjecture with analytical and numerical results for a specific example, the solution of generalized Riemann problems of a model system of equations with a fractional step scheme in which Godunov's method is coupled with the backward Euler method. We also apply our ideas to the numerical solution of stiff detonation problems. 1. Introduction. Hyperbolic systems of conservation laws with relaxation ...
Gravity & Hydrodynamics: Lectures on the fluidgravity correspondence
, 2009
"... We discuss recent developments in the hydrodynamic description of strongly coupled conformal field theories using the AdS/CFT correspondence. In particular, we review aspects of the fluidgravity correspondence which provides a map between a class of inhomogeneous, dynamical, black hole solutions in ..."
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Cited by 73 (1 self)
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We discuss recent developments in the hydrodynamic description of strongly coupled conformal field theories using the AdS/CFT correspondence. In particular, we review aspects of the fluidgravity correspondence which provides a map between a class of inhomogeneous, dynamical, black hole solutions in asymptotically AdS spacetimes and arbitrary fluid flows in the strongly interacting boundary field theory. We explain how the geometric duals to the fluid dynamics are constructed in a boundary derivative expansion and use the construction to extract the hydrodynamic transport coefficients. In addition we also describe the recent developments extending the correspondence to incorporate matter fields and to nonrelativistic systems. Based on