508 research outputs found
Fluid Simulations with Localized Boltzmann Upscaling by Direct Simulation Monte-Carlo
In the present work, we present a novel numerical algorithm to couple the
Direct Simulation Monte Carlo method (DSMC) for the solution of the Boltzmann
equation with a finite volume like method for the solution of the Euler
equations. Recently we presented in [14],[16],[17] different methodologies
which permit to solve fluid dynamics problems with localized regions of
departure from thermodynamical equilibrium. The methods rely on the
introduction of buffer zones which realize a smooth transition between the
kinetic and the fluid regions. In this paper we extend the idea of buffer zones
and dynamic coupling to the case of the Monte Carlo methods. To facilitate the
coupling and avoid the onset of spurious oscillations in the fluid regions
which are consequences of the coupling with a stochastic numerical scheme, we
use a new technique which permits to reduce the variance of the particle
methods [11]. In addition, the use of this method permits to obtain estimations
of the breakdowns of the fluid models less affected by fluctuations and
consequently to reduce the kinetic regions and optimize the coupling. In the
last part of the paper several numerical examples are presented to validate the
method and measure its computational performances
Turbulent Coronal Heating Mechanisms: Coupling of Dynamics and Thermodynamics
Context. Photospheric motions shuffle the footpoints of the strong axial
magnetic field that threads coronal loops giving rise to turbulent nonlinear
dynamics characterized by the continuous formation and dissipation of
field-aligned current sheets where energy is deposited at small-scales and the
heating occurs. Previous studies show that current sheets thickness is orders
of magnitude smaller than current state of the art observational resolution
(~700 km).
Aim. In order to understand coronal heating and interpret correctly
observations it is crucial to study the thermodynamics of such a system where
energy is deposited at unresolved small-scales.
Methods. Fully compressible three-dimensional magnetohydrodynamic simulations
are carried out to understand the thermodynamics of coronal heating in the
magnetically confined solar corona.
Results. We show that temperature is highly structured at scales below
observational resolution and nonhomogeneously distributed so that only a
fraction of the coronal mass and volume gets heated at each time.
Conclusions. This is a multi-thermal system where hotter and cooler plasma
strands are found one next to the other also at sub-resolution scales and
exhibit a temporal dynamics.Comment: A&A Letter, in pres
Velocity and energy relaxation in two-phase flows
In the present study we investigate analytically the process of velocity and
energy relaxation in two-phase flows. We begin our exposition by considering
the so-called six equations two-phase model [Ishii1975, Rovarch2006]. This
model assumes each phase to possess its own velocity and energy variables.
Despite recent advances, the six equations model remains computationally
expensive for many practical applications. Moreover, its advection operator may
be non-hyperbolic which poses additional theoretical difficulties to construct
robust numerical schemes |Ghidaglia et al, 2001]. In order to simplify this
system, we complete momentum and energy conservation equations by relaxation
terms. When relaxation characteristic time tends to zero, velocities and
energies are constrained to tend to common values for both phases. As a result,
we obtain a simple two-phase model which was recently proposed for simulation
of violent aerated flows [Dias et al, 2010]. The preservation of invariant
regions and incompressible limit of the simplified model are also discussed.
Finally, several numerical results are presented.Comment: 37 pages, 10 figures. Other authors papers can be downloaded at
http://www.lama.univ-savoie.fr/~dutykh
The subcritical baroclinic instability in local accretion disc models
(abridged) Aims: We present new results exhibiting a subcritical baroclinic
instability (SBI) in local shearing box models. We describe the 2D and 3D
behaviour of this instability using numerical simulations and we present a
simple analytical model describing the underlying physical process.
Results: A subcritical baroclinic instability is observed in flows stable for
the Solberg-Hoiland criterion using local simulations. This instability is
found to be a nonlinear (or subcritical) instability, which cannot be described
by ordinary linear approaches. It requires a radial entropy gradient weakly
unstable for the Schwartzchild criterion and a strong thermal diffusivity (or
equivalently a short cooling time). In compressible simulations, the
instability produces density waves which transport angular momentum outward
with typically alpha<3e-3, the exact value depending on the background
temperature profile. Finally, the instability survives in 3D, vortex cores
becoming turbulent due to parametric instabilities.
Conclusions: The subcritical baroclinic instability is a robust phenomenon,
which can be captured using local simulations. The instability survives in 3D
thanks to a balance between the 2D SBI and 3D parametric instabilities.
Finally, this instability can lead to a weak outward transport of angular
momentum, due to the generation of density waves by the vortices.Comment: 12 pages, 17 figures, Accepted in A&
Theoretical and numerical comparison of hyperelastic and hypoelastic formulations for Eulerian non-linear elastoplasticity
The aim of this paper is to compare a hyperelastic with a hypoelastic model
describing the Eulerian dynamics of solids in the context of non-linear
elastoplastic deformations. Specifically, we consider the well-known
hypoelastic Wilkins model, which is compared against a hyperelastic model based
on the work of Godunov and Romenski. First, we discuss some general conceptual
differences between the two approaches. Second, a detailed study of both models
is proposed, where differences are made evident at the aid of deriving a
hypoelastic-type model corresponding to the hyperelastic model and a particular
equation of state used in this paper. Third, using the same high order ADER
Finite Volume and Discontinuous Galerkin methods on fixed and moving
unstructured meshes for both models, a wide range of numerical benchmark test
problems has been solved. The numerical solutions obtained for the two
different models are directly compared with each other. For small elastic
deformations, the two models produce very similar solutions that are close to
each other. However, if large elastic or elastoplastic deformations occur, the
solutions present larger differences.Comment: 14 figure
The Moment Guided Monte Carlo method for the Boltzmann equation
In this work we propose a generalization of the Moment Guided Monte Carlo
method developed in [11]. This approach permits to reduce the variance of the
particle methods through a matching with a set of suitable macroscopic moment
equations. In order to guarantee that the moment equations provide the correct
solutions, they are coupled to the kinetic equation through a non equilibrium
term. Here, at the contrary to the previous work in which we considered the
simplified BGK operator, we deal with the full Boltzmann operator. Moreover, we
introduce an hybrid setting which permits to entirely remove the resolution of
the kinetic equation in the limit of infinite number of collisions and to
consider only the solution of the compressible Euler equation. This
modification additionally reduce the statistical error with respect to our
previous work and permits to perform simulations of non equilibrium gases using
only a few number of particles. We show at the end of the paper several
numerical tests which prove the efficiency and the low level of numerical noise
of the method.Comment: arXiv admin note: text overlap with arXiv:0908.026
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