112,257 research outputs found
A Fluid-Dynamical Subgrid Scale Model for Highly Compressible Astrophysical Turbulence
We formulate and implement the Euler equations with SGS dynamics and provide
numerical tests of an SGS turbulence energy model that predicts the turbulent
pressure of unresolved velocity fluctuations and the rate of dissipation for
highly compressible turbulence. We test closures for the turbulence energy
cascade by filtering data from high-resolution simulations of forced isothermal
and adiabatic turbulence. Optimal properties and an excellent correlation are
found for a linear combination of the eddy-viscosity closure that is employed
in LES of weakly compressible turbulence and a term that is non-linear in the
Jacobian matrix of the velocity. Using this mixed closure, the SGS turbulence
energy model is validated in LES of turbulence with stochastic forcing. It is
found that the SGS model satisfies several important requirements: 1. The mean
SGS turbulence energy follows a power law for varying grid scale. 2. The root
mean square (RMS) Mach number of the unresolved velocity fluctuations is
proportional to the RMS Mach number of the resolved turbulence, independent of
the forcing. 3. The rate of dissipation and the turbulence energy flux are
constant. Moreover, we discuss difficulties with direct estimates of the
turbulent pressure and the dissipation rate on the basis of resolved flow
quantities that have recently been proposed. In combination with the energy
injection by stellar feedback and other unresolved processes, the proposed SGS
model is applicable to a variety of problems in computational astrophysics.
Computing the SGS turbulence energy, the treatment of star formation and
stellar feedback in galaxy simulations can be improved. Further, we expect that
the turbulent pressure on the grid scale affects the stability of gas against
gravitational collapse.Comment: 19 pages, 16 figures, submitted to A&
Large-N expansions applied to gravitational clustering
We develop a path-integral formalism to study the formation of large-scale
structures in the universe. Starting from the equations of motion of
hydrodynamics (single-stream approximation) we derive the action which
describes the statistical properties of the density and velocity fields for
Gaussian initial conditions. Then, we present large-N expansions (associated
with a generalization to N fields or with a semi-classical expansion) of the
path-integral defined by this action. This provides a systematic expansion for
two-point functions such as the response function and the usual two-point
correlation. We present the results of two such expansions (and related
variants) at one-loop order for a SCDM and a LCDM cosmology. We find that the
response function exhibits fast oscillations in the non-linear regime with an
amplitude which either follows the linear prediction (for the direct
steepest-descent scheme) or decays (for the 2PI effective action scheme). On
the other hand, the correlation function agrees with the standard one-loop
result in the quasi-linear regime and remains well-behaved in the highly
non-linear regime. This suggests that these large-N expansions could provide a
good framework to study the dynamics of gravitational clustering in the
non-linear regime. Moreover, the use of various expansion schemes allows one to
estimate their range of validity without the need of N-body simulations and
could provide a better accuracy in the weakly non-linear regime.Comment: 27 pages, published in A&
Some Key Developments in Computational Electromagnetics and their Attribution
Key developments in computational electromagnetics are proposed. Historical highlights are summarized concentrating on the two main approaches of differential and integral methods. This is seen as timely as a retrospective analysis is needed to minimize duplication and to help settle questions of attribution
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