7,738 research outputs found
Cluster-based reduced-order modelling of a mixing layer
We propose a novel cluster-based reduced-order modelling (CROM) strategy of
unsteady flows. CROM combines the cluster analysis pioneered in Gunzburger's
group (Burkardt et al. 2006) and and transition matrix models introduced in
fluid dynamics in Eckhardt's group (Schneider et al. 2007). CROM constitutes a
potential alternative to POD models and generalises the Ulam-Galerkin method
classically used in dynamical systems to determine a finite-rank approximation
of the Perron-Frobenius operator. The proposed strategy processes a
time-resolved sequence of flow snapshots in two steps. First, the snapshot data
are clustered into a small number of representative states, called centroids,
in the state space. These centroids partition the state space in complementary
non-overlapping regions (centroidal Voronoi cells). Departing from the standard
algorithm, the probabilities of the clusters are determined, and the states are
sorted by analysis of the transition matrix. Secondly, the transitions between
the states are dynamically modelled using a Markov process. Physical mechanisms
are then distilled by a refined analysis of the Markov process, e.g. using
finite-time Lyapunov exponent and entropic methods. This CROM framework is
applied to the Lorenz attractor (as illustrative example), to velocity fields
of the spatially evolving incompressible mixing layer and the three-dimensional
turbulent wake of a bluff body. For these examples, CROM is shown to identify
non-trivial quasi-attractors and transition processes in an unsupervised
manner. CROM has numerous potential applications for the systematic
identification of physical mechanisms of complex dynamics, for comparison of
flow evolution models, for the identification of precursors to desirable and
undesirable events, and for flow control applications exploiting nonlinear
actuation dynamics.Comment: 48 pages, 30 figures. Revised version with additional material.
Accepted for publication in Journal of Fluid Mechanic
Entropic Multi-Relaxation Models for Simulation of Fluid Turbulence
A recently introduced family of lattice Boltzmann (LB) models (Karlin,
B\"osch, Chikatamarla, Phys. Rev. E, 2014) is studied in detail for
incompressible two-dimensional flows. A framework for developing LB models
based on entropy considerations is laid out extensively. Second order rate of
convergence is numerically confirmed and it is demonstrated that these entropy
based models recover the Navier-Stokes solution in the hydrodynamic limit.
Comparison with the standard Bhatnagar-Gross-Krook (LBGK) and the entropic
lattice Boltzmann method (ELBM) demonstrates the superior stability and
accuracy for several benchmark flows and a range of grid resolutions and
Reynolds numbers. High Reynolds number regimes are investigated through the
simulation of two-dimensional turbulence, particularly for under-resolved
cases. Compared to resolved LBGK simulations, the presented class of LB models
demonstrate excellent performance and capture the turbulence statistics with
good accuracy.Comment: To be published in Proceedings of Discrete Simulation of Fluid
Dynamics DSFD 201
Relaxed micromorphic model of transient wave propagation in anisotropic band-gap metastructures
In this paper, we show that the transient waveforms arising from several
localised pulses in a micro-structured material can be reproduced by a
corresponding generalised continuum of the relaxed micromorphic type.
Specifically, we compare the dynamic response of a bounded micro-structured
material to that of bounded continua with special kinematic properties: (i) the
relaxed micromorphic continuum and (ii) an equivalent Cauchy linear elastic
continuum. We show that, while the Cauchy theory is able to describe the
overall behaviour of the metastructure only at low frequencies, the relaxed
micromorphic model goes far beyond by giving a correct description of the pulse
propagation in the frequency band-gap and at frequencies intersecting the
optical branches. In addition, we observe a computational time reduction
associated with the use of the relaxed micromorphic continuum, compared to the
sensible computational time needed to perform a transient computation in a
micro-structured domain
Coherent structures in a simulated turbulent mixing layer
A direct numerical simulation of a plane turbulent mixing layer has been performed. The simulation was initialized using two turbulent velocity fields obtained from direct numerical simulation of a turbulent boundary layer at momentum thickness Reynolds number 300 (Spalart, 1988). The mixing layer is allowed to evolve long enough for self-similar linear growth to occur, with the visual thickness Reynolds number reaching 14,000. The simulated flow is examined for evidence of the coherent structures expected in a mixing layer (rollers and rib vortices). Before the onset of self-similar growth, such structures are present with properties similar to the corresponding laminar or transitional structures. In the self-similar growth regime, however, only the rollers are present with no indication of rib vortices and no indication of conventional pairing. This results in a reduction of mixing and layer growth
Refraction of dispersive shock waves
We study a dispersive counterpart of the classical gas dynamics problem of
the interaction of a shock wave with a counter-propagating simple rarefaction
wave often referred to as the shock wave refraction. The refraction of a
one-dimensional dispersive shock wave (DSW) due to its head-on collision with
the centred rarefaction wave (RW) is considered in the framework of defocusing
nonlinear Schr\"odinger (NLS) equation. For the integrable cubic nonlinearity
case we present a full asymptotic description of the DSW refraction by
constructing appropriate exact solutions of the Whitham modulation equations in
Riemann invariants. For the NLS equation with saturable nonlinearity, whose
modulation system does not possess Riemann invariants, we take advantage of the
recently developed method for the DSW description in non-integrable dispersive
systems to obtain main physical parameters of the DSW refraction. The key
features of the DSW-RW interaction predicted by our modulation theory analysis
are confirmed by direct numerical solutions of the full dispersive problem.Comment: 45 pages, 23 figures, minor revisio
Favard Theory and fredholm alternative for disconjugate recurrent second order equations
ProducciĂłn CientĂficaWe discuss the existence of a Fredholm--type Alternative for a recurrent second order linear equation, which is disconjugate in a strong sense. The basic result is about bounded solutions of equations with bounded coefficients: it depends on kinematic similarities that allow to reduce the problem to a pair of very simple normal forms. Then the result is specialized to recurrent equations, by means of Favard theory.MINECO/FEDER MTM2015-6633
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