1,222 research outputs found
Comparison of numerical solvers for anisotropic diffusion equations arising in plasma physics
International audienceThis work is devoted to the comparison of numerical schemes to approximate anisotropic diffusion problems arising in tokamak plasma physics. We focus on the spatial approximation by using finite volume method and on the time discretization. This latter point is delicate since the use of explicit integrators leads to a severe restriction on the time step. Then, implicit and semi-implicit schemes are coupled to finite volumes space discretization and are compared for some classical problems relevant for magnetically confined plasmas. It appears that the semi-implicit approaches (using ARK methods or directional splitting) turn out to be the most efficient on the numerical results, especially when nonlinear problems are studied on refined meshes, using high order methods in space
An implicit scheme for solving the anisotropic diffusion of heat and cosmic rays in the RAMSES code
Astrophysical plasmas are subject to a tight connection between magnetic
fields and the diffusion of particles, which leads to an anisotropic transport
of energy. Under the fluid assumption, this effect can be reduced to an
advection-diffusion equation augmenting the equations of magnetohydrodynamics.
We introduce a new method for solving the anisotropic diffusion equation using
an implicit finite-volume method with adaptive mesh refinement and adaptive
time-stepping in the RAMSES code. We apply this numerical solver to the
diffusion of cosmic ray energy, and diffusion of heat carried by electrons,
which couple to the ion temperature. We test this new implementation against
several numerical experiments and apply it to a simple supernova explosion with
a uniform magnetic field.Comment: 11 pages, 10 figures, A&
Kinetic Solvers with Adaptive Mesh in Phase Space
An Adaptive Mesh in Phase Space (AMPS) methodology has been developed for
solving multi-dimensional kinetic equations by the discrete velocity method. A
Cartesian mesh for both configuration (r) and velocity (v) spaces is produced
using a tree of trees data structure. The mesh in r-space is automatically
generated around embedded boundaries and dynamically adapted to local solution
properties. The mesh in v-space is created on-the-fly for each cell in r-space.
Mappings between neighboring v-space trees implemented for the advection
operator in configuration space. We have developed new algorithms for solving
the full Boltzmann and linear Boltzmann equations with AMPS. Several recent
innovations were used to calculate the discrete Boltzmann collision integral
with dynamically adaptive mesh in velocity space: importance sampling,
multi-point projection method, and the variance reduction method. We have
developed an efficient algorithm for calculating the linear Boltzmann collision
integral for elastic and inelastic collisions in a Lorentz gas. New AMPS
technique has been demonstrated for simulations of hypersonic rarefied gas
flows, ion and electron kinetics in weakly ionized plasma, radiation and light
particle transport through thin films, and electron streaming in
semiconductors. We have shown that AMPS allows minimizing the number of cells
in phase space to reduce computational cost and memory usage for solving
challenging kinetic problems
Scalable explicit implementation of anisotropic diffusion with Runge-Kutta-Legendre super-time-stepping
An important ingredient in numerical modelling of high temperature magnetised
astrophysical plasmas is the anisotropic transport of heat along magnetic field
lines from higher to lower temperatures.Magnetohydrodynamics (MHD) typically
involves solving the hyperbolic set of conservation equations along with the
induction equation. Incorporating anisotropic thermal conduction requires to
also treat parabolic terms arising from the diffusion operator. An explicit
treatment of parabolic terms will considerably reduce the simulation time step
due to its dependence on the square of the grid resolution () for
stability. Although an implicit scheme relaxes the constraint on stability, it
is difficult to distribute efficiently on a parallel architecture. Treating
parabolic terms with accelerated super-time stepping (STS) methods has been
discussed in literature but these methods suffer from poor accuracy (first
order in time) and also have difficult-to-choose tuneable stability parameters.
In this work we highlight a second order (in time) Runge Kutta Legendre (RKL)
scheme (first described by Meyer et. al. 2012) that is robust, fast and
accurate in treating parabolic terms alongside the hyperbolic conversation
laws. We demonstrate its superiority over the first order super time stepping
schemes with standard tests and astrophysical applications. We also show that
explicit conduction is particularly robust in handling saturated thermal
conduction. Parallel scaling of explicit conduction using RKL scheme is
demonstrated up to more than processors.Comment: 15 pages, 9 figures, incorporated comments from the referee. This
version is now accepted for publication in MNRA
Diffusion of energetic particles in turbulent MHD plasmas
In this paper we investigate the transport of energetic particles in
turbulent plasmas. A numerical approach is used to simulate the effect of the
background plasma on the motion of energetic protons. The background plasma is
in a dynamically turbulent state found from numerical MHD simulations, where we
use parameters typical for the heliosphere. The implications for the transport
parameters (i.e. pitch-angle diffusion coefficients and mean free path) are
calculated and deviations from the quasi-linear theory are discussed.Comment: Accepted for publication in Ap
The Inertial Range of Turbulence in the Inner Heliosheath and in the Local Interstellar Medium
The governing mechanisms of magnetic field annihilation in the outer heliosphere is an intriguing topic. It is currently believed that the turbulent fluctuations pervade the inner heliosheath (IHS) and the Local Interstellar Medium (LISM). Turbulence, magnetic reconnection, or their reciprocal link may be responsible for magnetic energy conversion in the IHS.
As 1-day averaged data are typically used, the present literature mainly concerns large-scale analysis and does not describe inertial-cascade dynamics of turbulence in the IHS. Moreover, lack of spectral analysis make IHS dynamics remain critically understudied. Our group showed that 48-s MAG data from the Voyager mission are appropriate for a power spectral analysis over a frequency range of five decades, from 5e-8 Hz to 1e-2 Hz [Gallana et al., JGR 121 (2016)]. Special spectral estimation techniques are used to deal with the large amount of missing data (70%). We provide the first clear evidence of an inertial-cascade range of turbulence (spectral index is between -2 and -1.5). A spectral break at about 1e-5 Hz is found to separate the inertial range from the enegy-injection range (1/f energy decay). Instrumental noise bounds our investigation to frequencies lower than 5e-4 Hz. By considering several consecutive periods after 2009 at both V1 and V2, we show that the extension and the spectral energy decay of these two regimes may be indicators of IHS regions governed by different physical processes. We describe fluctuations’ regimes in terms of spectral energy density, anisotropy, compressibility, and statistical analysis of intermittency.
In the LISM, it was theorized that pristine interstellar turbulence may coexist with waves from the IHS, however this is still a debated topic. We observe that the fluctuating magnetic energy cascades as a power law with spectral index in the range [-1.35, -1.65] in the whole range of frequencies unaffected by noise. No spectral break is observed, nor decaying turbulence
A mimetic finite difference based quasi-static magnetohydrodynamic solver for force-free plasmas in tokamak disruptions
Force-free plasmas are a good approximation where the plasma pressure is tiny
compared with the magnetic pressure, which is the case during the cold vertical
displacement event (VDE) of a major disruption in a tokamak. On time scales
long compared with the transit time of Alfven waves, the evolution of a
force-free plasma is most efficiently described by the quasi-static
magnetohydrodynamic (MHD) model, which ignores the plasma inertia. Here we
consider a regularized quasi-static MHD model for force-free plasmas in tokamak
disruptions and propose a mimetic finite difference (MFD) algorithm. The full
geometry of an ITER-like tokamak reactor is treated, with a blanket module
region, a vacuum vessel region, and the plasma region. Specifically, we develop
a parallel, fully implicit, and scalable MFD solver based on PETSc and its
DMStag data structure for the discretization of the five-field quasi-static
perpendicular plasma dynamics model on a 3D structured mesh. The MFD spatial
discretization is coupled with a fully implicit DIRK scheme. The algorithm
exactly preserves the divergence-free condition of the magnetic field under the
resistive Ohm's law. The preconditioner employed is a four-level fieldsplit
preconditioner, which is created by combining separate preconditioners for
individual fields, that calls multigrid or direct solvers for sub-blocks or
exact factorization on the separate fields. The numerical results confirm the
divergence-free constraint is strongly satisfied and demonstrate the
performance of the fieldsplit preconditioner and overall algorithm. The
simulation of ITER VDE cases over the actual plasma current diffusion time is
also presented.Comment: 43 page
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