Perfect fluid

Summary

In physics, a perfect fluid is a fluid that can be completely characterized by its rest frame mass density \rho_m and isotropic pressure p. Real fluids are "sticky" and contain (and conduct) heat. Perfect fluids are idealized models in which these possibilities are neglected. Specifically, perfect fluids have no shear stresses, viscosity, or heat conduction. Quark–gluon plasma is the closest known substance to a perfect fluid. In space-positive metric signature tensor notation, the stress–energy tensor of a perfect fluid can be written in the form :T^{\mu\nu} = \left( \rho_m + \frac{p}{c^2} \right) , U^\mu U^\nu + p , \eta^{\mu\nu}, where U is the 4-velocity vector field of the fluid and where \eta_{\mu \nu} = \operatorname{diag}(-1,1,1,1) is the metric tensor of Minkowski spacetime. In time-positive metric signature tensor notation, the stress–energy tensor of a perfect fluid can be written in the form :T^{\mu\nu} = \left( \rho_\text

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Geometric, variational discretization of continuum theories

Mathieu Desbrun

This study derives geometric, variational discretization of continuum theories arising in fluid dynamics, magnetohydrodynamics (MHD), and the dynamics of complex fluids. A central role in these discretizations is played by the geometric formulation of fluid dynamics, which views solutions to the governing equations for perfect fluid flow as geodesics on the group of volume-preserving diffeomorphisms of the fluid domain. Inspired by this framework, we construct a finite-dimensional approximation to the diffeomorphism group and its Lie algebra, thereby permitting a variational temporal discretization of geodesics on the spatially discretized diffeomorphism group. The extension to MHD and complex fluid flow is then made through an appeal to the theory of Euler-Poincare systems with advection, which provides a generalization of the variational formulation of ideal fluid flow to fluids with one or more advected parameters. Upon deriving a family of structured integrators for these systems, we test their performance via a numerical implementation of the update schemes on a cartesian grid. Among the hallmarks of these new numerical methods are exact preservation of momenta arising from symmetries, automatic satisfaction of solenoidal constraints on vector fields, good long-term energy behavior, robustness with respect to the spatial and temporal resolution of the discretization, and applicability to irregular meshes. (C) 2011 Elsevier B.V. All rights reserved.

2011

The Weyssenhoff fluid is a perfect fluid with spin where the spin of the matter fields is the source of torsion in an Einstein–Cartan framework. Obukhov and Korotky showed that this fluid can be described as an effective fluid with spin in general relativity. A dynamical analysis of such a fluid is performed in a gauge-invariant manner using the 1 + 3 covariant approach. This yields the propagation and constraint equations for the set of dynamical variables. A verification of these equations is performed for the special case of irrotational flow with zero peculiar acceleration by evolving the constraints.

Institute of Physics2007

First-order adiabatic perturbations of a perfect fluid about a general FLRW background using the 1+3 covariant and gauge-invariant formalism

Sylvain Bréchet

An analysis of adiabatic perturbations of a perfect fluid is performed to first-order about a general FLRW background using the 1+3 covariant and gauge-invariant formalism. The analog of the Mukhanov-Sasaki variable and the canonical variables needed to quantise respectively the scalar and tensor perturbations in a general FLRW background space-time are identified. The dynamics of the vector perturbations is also discussed.

American Physical Society2009