scholarly journals Second order hydrodynamic coefficients from 3-point stress tensor correlators via AdS/CFT

2011 ◽  
Vol 2011 (10) ◽  
Author(s):  
Peter Arnold ◽  
Diana Vaman ◽  
Chaolun Wu ◽  
Wei Xiao
Keyword(s):  
Stress Tensor ◽  
Second Order ◽  
Hydrodynamic Coefficients

scholarly journals Three-Dimensional Central Moment Lattice Boltzmann Method on a Cuboid Lattice for Anisotropic and Inhomogeneous Flows

Fluids ◽  
2021 ◽  
Vol 6 (9) ◽  
pp. 326
Author(s):  
Eman Yahia ◽  
William Schupbach ◽  
Kannan N. Premnath
Keyword(s):  
Stress Tensor ◽  
Shear Viscosity ◽  
Lattice Boltzmann ◽  
Central Moment ◽  
Second Order ◽  
Memory Storage ◽  
Viscous Stress ◽  
Viscous Stress Tensor ◽  
Cubic Lattice ◽  
Aspect Ratios

Lattice Boltzmann (LB) methods are usually developed on cubic lattices that discretize the configuration space using uniform grids. For efficient computations of anisotropic and inhomogeneous flows, it would be beneficial to develop LB algorithms involving the collision-and-stream steps based on orthorhombic cuboid lattices. We present a new 3D central moment LB scheme based on a cuboid D3Q27 lattice. This scheme involves two free parameters representing the ratios of the characteristic particle speeds along the two directions with respect to those in the remaining direction, and these parameters are referred to as the grid aspect ratios. Unlike the existing LB schemes for cuboid lattices, which are based on orthogonalized raw moments, we construct the collision step based on the relaxation of central moments and avoid the orthogonalization of moment basis, which leads to a more robust formulation. Moreover, prior cuboid LB algorithms prescribe the mappings between the distribution functions and raw moments before and after collision by using a moment basis designed to separate the trace of the second order moments (related to bulk viscosity) from its other components (related to shear viscosity), which lead to cumbersome relations for the transformations. By contrast, in our approach, the bulk and shear viscosity effects associated with the viscous stress tensor are naturally segregated only within the collision step and not for such mappings, while the grid aspect ratios are introduced via simpler pre- and post-collision diagonal scaling matrices in the above mappings. These lead to a compact approach, which can be interpreted based on special matrices. It also results in a modular 3D LB scheme on the cuboid lattice, which allows the existing cubic lattice implementations to be readily extended to those based on the more general cuboid lattices. To maintain the isotropy of the viscous stress tensor of the 3D Navier–Stokes equations using the cuboid lattice, corrections for eliminating the truncation errors resulting from the grid anisotropy as well as those from the aliasing effects are derived using a Chapman–Enskog analysis. Such local corrections, which involve the diagonal components of the velocity gradient tensor and are parameterized by two grid aspect ratios, augment the second order moment equilibria in the collision step. We present a numerical study validating the accuracy of our approach for various benchmark problems at different grid aspect ratios. In addition, we show that our 3D cuboid central moment LB method is numerically more robust than its corresponding raw moment formulation. Finally, we demonstrate the effectiveness of the 3D cuboid central moment LB scheme for the simulations of anisotropic and inhomogeneous flows and show significant savings in memory storage and computational cost when used in lieu of that based on the cubic lattice.

The gravitational-electromagnetic Noether operator and the second-order energy flux

1991 ◽  
Vol 435 (1895) ◽  
pp. 635-644 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Stress Tensor ◽  
Stationary Solution ◽  
Energy Flux ◽  
Second Order ◽  
First Order ◽  
Energy Current ◽  
Order Energy

The Noether operator for gravity is recalled and that for the electromagnetic field derived, its difference from the electromagnetic stress tensor being pointed out. It is then shown how the Noether operator’s defining equation leads, in the case of perturbations about a stationary solution, to a conserved energy current depending quadratically on the first-order perturbations alone. The formal background of the paper by Chandrasekhar & Ferrari is thereby clarified.

scholarly journals Enhancement of Turbulent Viscosity by Global Magnetic Fields in Accretion Disks

1998 ◽  
Vol 188 ◽  
pp. 412-412
Author(s):  
Yasushi Nakao
Keyword(s):  
Magnetic Fields ◽  
Stress Tensor ◽  
Accretion Disks ◽  
Turbulent Viscosity ◽  
A Priori ◽  
Vertical Direction ◽  
Direct Interaction ◽  
Second Order ◽  
Mhd Turbulence ◽  
Maxwell Stress Tensor

A model of magnetohydrodynamic (MHD) turbulence in accretion disks with global magnetic fields is constructed using a second-order closure modeling of turbulence. The transport equations of the Reynolds stress tensor, the Maxwell stress tensor, and the cross-helicity tensor (the correlation of velocity fluctuation and magnetic fluctuation) are closed by second-order quantities using atwo-scale direct interaction approximation(TSDIA). The quantities appearing these equations are considered to be those averaged in the vertical direction of the disks. The turbulence is assumed to be stationary. We are interested only in the effects of the global magnetic fields on the turbulence in the disks, i.e., no dynamo processes are considered, and the global magnetic fields are supposed to be embedded in the diska priori.

Hydrodynamics of spin currents

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Angel Domingo Gallegos ◽  
Umut Gürsoy ◽  
Amos Yarom
Keyword(s):  
Stress Tensor ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Spin Current ◽  
Second Order ◽  
Relativistic Hydrodynamics ◽  
Hydrodynamic Equations ◽  
Spin Currents ◽  
Dynamical Spin ◽  
Good Agreement

We study relativistic hydrodynamics in the presence of a non vanishing spin potential. Using a variety of techniques we carry out an exhaustive analysis, and identify the constitutive relations for the stress tensor and spin current in such a setup, allowing us to write the hydrodynamic equations of motion to second order in derivatives. We then solve the equations of motion in a certain dynamical spin limit and in a perturbative setup and find surprisingly good agreement with measurements of global \LambdaΛ-hyperon polarization carried out at RHIC.

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