59 research outputs found
Multiphysics simulations of collisionless plasmas
Collisionless plasmas, mostly present in astrophysical and space
environments, often require a kinetic treatment as given by the Vlasov
equation. Unfortunately, the six-dimensional Vlasov equation can only be solved
on very small parts of the considered spatial domain. However, in some cases,
e.g. magnetic reconnection, it is sufficient to solve the Vlasov equation in a
localized domain and solve the remaining domain by appropriate fluid models. In
this paper, we describe a hierarchical treatment of collisionless plasmas in
the following way. On the finest level of description, the Vlasov equation is
solved both for ions and electrons. The next courser description treats
electrons with a 10-moment fluid model incorporating a simplified treatment of
Landau damping. At the boundary between the electron kinetic and fluid region,
the central question is how the fluid moments influence the electron
distribution function. On the next coarser level of description the ions are
treated by an 10-moment fluid model as well. It may turn out that in some
spatial regions far away from the reconnection zone the temperature tensor in
the 10-moment description is nearly isotopic. In this case it is even possible
to switch to a 5-moment description. This change can be done separately for
ions and electrons. To test this multiphysics approach, we apply this full
physics-adaptive simulations to the Geospace Environmental Modeling (GEM)
challenge of magnetic reconnection.Comment: 13 pages, 5 figure
Lagrangian and geometric analysis of finite-time Euler singularities
We present a numerical method of analyzing possibly singular incompressible
3D Euler flows using massively parallel high-resolution adaptively refined
numerical simulations up to 8192^3 mesh points. Geometrical properties of
Lagrangian vortex line segments are used in combination with analytical
non-blowup criteria by Deng et al [Commun. PDE 31 (2006)] to reliably
distinguish between singular and near-singular flow evolution. We then apply
the presented technique to a class of high-symmetry initial conditions and
present numerical evidence against the formation of a finite-time singularity
in this case.Comment: arXiv admin note: text overlap with arXiv:1210.253
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
Temperature gradient driven heat flux closure in fluid simulations of collisionless reconnection
Recent efforts to include kinetic effects in fluid simulations of plasmas
have been very promising. Concerning collisionless magnetic reconnection, it
has been found before that damping of the pressure tensor to isotropy leads to
good agreement with kinetic runs in certain scenarios. An accurate
representation of kinetic effects in reconnection was achieved in a study by
Wang et al. (Phys. Plasmas, volume 22, 2015, 012108) with a closure derived
from earlier work by Hammett and Perkins (PRL, volume 64, 1990, 3019). Here,
their approach is analyzed on the basis of heat flux data from a Vlasov
simulation. As a result, we propose a new local closure in which heat flux is
driven by temperature gradients. That way, a more realistic approximation of
Landau damping in the collisionless regime is achieved. Previous issues are
addressed and the agreement with kinetic simulations in different reconnection
setups is improved significantly. To the authors' knowledge, the new fluid
model is the first to perform well in simulations of the coalescence of large
magnetic islands.Comment: 14 pages, 7 figure
Multiscale velocity correlations in turbulence and Burgers turbulence: Fusion rules, Markov processes in scale, and multifractal predictions
We compare different approaches towards an effective description of
multi-scale velocity field correlations in turbulence. Predictions made by the
operator product expansion, the so-called fusion rules, are placed in
juxtaposition to an approach that interprets the turbulent energy cascade in
terms of a Markov process of velocity increments in scale. We explicitly show
that the fusion rules are a direct consequence of the Markov property provided
that the structure functions exhibit scaling in the inertial range.
Furthermore, the limit case of joint velocity gradient and velocity increment
statistics is discussed and put into the context of the notion of dissipative
anomaly. We generalize a prediction made by the multifractal (MF) approach
derived in [Phys. Rev. Lett. 80, 3244 (1998)] to correlations among inertial
range velocity increment and velocity gradients of any order. We show that for
the case of squared velocity gradients such a relation can be derived from
"first principles" in the case of Burgers equation. Our results are benchmarked
by intensive direct numerical simulations of Burgers turbulence.Comment: 18 pages, 6 figure
Adaptive Mesh Refinement for Singular Current Sheets in Incompressible Magnetohydrodynamic Flows
The formation of current sheets in ideal incompressible magnetohydrodynamic
flows in two dimensions is studied numerically using the technique of adaptive
mesh refinement. The growth of current density is in agreement with simple
scaling assumptions. As expected, adaptive mesh refinement shows to be very
efficient for studying singular structures compared to non-adaptive treatments.Comment: 8 pages RevTeX, 13 Postscript figure
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