19,721 research outputs found
Algorithms and Models for Turbulence Not at Statistical Equilibrium
Standard eddy viscosity models, while robust, cannot represent backscatter
and have severe difficulties with complex turbulence not at statistical
equilibrium. This report gives a new derivation of eddy viscosity models from
an equation for the evolution of variance in a turbulent flow. The new
derivation also shows how to correct eddy viscosity models. The report proves
the corrected models preserve important features of the true Reynolds stresses.
It gives algorithms for their discretization including a minimally invasive
modular step to adapt an eddy viscosity code to the extended models. A
numerical test is given with the usual and over diffusive Smagorinsky model.
The correction (scaled by ) does successfully exhibit intermittent
backscatter.Comment: 18 pages, 2 figure
The prospect of using LES and DES in engineering design, and the research required to get there
In this paper we try to look into the future to divine how large eddy and
detached eddy simulations (LES and DES, respectively) will be used in the
engineering design process about 20-30 years from now. Some key challenges
specific to the engineering design process are identified, and some of the
critical outstanding problems and promising research directions are discussed.Comment: accepted for publication in the Royal Society Philosophical
Transactions
The instanton method and its numerical implementation in fluid mechanics
A precise characterization of structures occurring in turbulent fluid flows
at high Reynolds numbers is one of the last open problems of classical physics.
In this review we discuss recent developments related to the application of
instanton methods to turbulence. Instantons are saddle point configurations of
the underlying path integrals. They are equivalent to minimizers of the related
Freidlin-Wentzell action and known to be able to characterize rare events in
such systems. While there is an impressive body of work concerning their
analytical description, this review focuses on the question on how to compute
these minimizers numerically. In a short introduction we present the relevant
mathematical and physical background before we discuss the stochastic Burgers
equation in detail. We present algorithms to compute instantons numerically by
an efficient solution of the corresponding Euler-Lagrange equations. A second
focus is the discussion of a recently developed numerical filtering technique
that allows to extract instantons from direct numerical simulations. In the
following we present modifications of the algorithms to make them efficient
when applied to two- or three-dimensional fluid dynamical problems. We
illustrate these ideas using the two-dimensional Burgers equation and the
three-dimensional Navier-Stokes equations
Gravitational Collapse in Turbulent Molecular Clouds. I. Gasdynamical Turbulence
Observed molecular clouds often appear to have very low star formation
efficiencies and lifetimes an order of magnitude longer than their free-fall
times. Their support is attributed to the random supersonic motions observed in
them. We study the support of molecular clouds against gravitational collapse
by supersonic, gas dynamical turbulence using direct numerical simulation.
Computations with two different algorithms are compared: a particle-based,
Lagrangian method (SPH), and a grid-based, Eulerian, second-order method
(ZEUS). The effects of both algorithm and resolution can be studied with this
method. We find that, under typical molecular cloud conditions, global collapse
can indeed be prevented, but density enhancements caused by strong shocks
nevertheless become gravitationally unstable and collapse into dense cores and,
presumably, stars. The occurance and efficiency of local collapse decreases as
the driving wave length decreases and the driving strength increases. It
appears that local collapse can only be prevented entirely with unrealistically
short wave length driving, but observed core formation rates can be reproduced
with more realistic driving. At high collapse rates, cores are formed on short
time scales in coherent structures with high efficiency, while at low collapse
rates they are scattered randomly throughout the region and exhibit
considerable age spread. We suggest that this naturally explains the observed
distinction between isolated and clustered star formation.Comment: Minor revisions in response to referee, thirteen figures, accepted to
Astrophys.
Optimisation of confinement in a fusion reactor using a nonlinear turbulence model
The confinement of heat in the core of a magnetic fusion reactor is optimised
using a multidimensional optimisation algorithm. For the first time in such a
study, the loss of heat due to turbulence is modelled at every stage using
first-principles nonlinear simulations which accurately capture the turbulent
cascade and large-scale zonal flows. The simulations utilise a novel approach,
with gyrofluid treatment of the small-scale drift waves and gyrokinetic
treatment of the large-scale zonal flows. A simple near-circular equilibrium
with standard parameters is chosen as the initial condition. The figure of
merit, fusion power per unit volume, is calculated, and then two control
parameters, the elongation and triangularity of the outer flux surface, are
varied, with the algorithm seeking to optimise the chosen figure of merit. A
two-fold increase in the plasma power per unit volume is achieved by moving to
higher elongation and strongly negative triangularity.Comment: 32 pages, 8 figures, accepted to JP
- …