989 research outputs found
High-order conservative reconstruction schemes for finite volume methods in cylindrical and spherical coordinates
High-order reconstruction schemes for the solution of hyperbolic conservation
laws in orthogonal curvilinear coordinates are revised in the finite volume
approach. The formulation employs a piecewise polynomial approximation to the
zone-average values to reconstruct left and right interface states from within
a computational zone to arbitrary order of accuracy by inverting a
Vandermonde-like linear system of equations with spatially varying
coefficients. The approach is general and can be used on uniform and
non-uniform meshes although explicit expressions are derived for polynomials
from second to fifth degree in cylindrical and spherical geometries with
uniform grid spacing. It is shown that, in regions of large curvature, the
resulting expressions differ considerably from their Cartesian counterparts and
that the lack of such corrections can severely degrade the accuracy of the
solution close to the coordinate origin. Limiting techniques and monotonicity
constraints are revised for conventional reconstruction schemes, namely, the
piecewise linear method (PLM), third-order weighted essentially non-oscillatory
(WENO) scheme and the piecewise parabolic method (PPM).
The performance of the improved reconstruction schemes is investigated in a
number of selected numerical benchmarks involving the solution of both scalar
and systems of nonlinear equations (such as the equations of gas dynamics and
magnetohydrodynamics) in cylindrical and spherical geometries in one and two
dimensions. Results confirm that the proposed approach yields considerably
smaller errors, higher convergence rates and it avoid spurious numerical
effects at a symmetry axis.Comment: 37 pages, 12 Figures. Accepted for publication in Journal of
Compuational Physic
A Second-Order Unsplit Godunov Scheme for Cell-Centered MHD: the CTU-GLM scheme
We assess the validity of a single step Godunov scheme for the solution of
the magneto-hydrodynamics equations in more than one dimension. The scheme is
second-order accurate and the temporal discretization is based on the
dimensionally unsplit Corner Transport Upwind (CTU) method of Colella. The
proposed scheme employs a cell-centered representation of the primary fluid
variables (including magnetic field) and conserves mass, momentum, magnetic
induction and energy. A variant of the scheme, which breaks momentum and energy
conservation, is also considered. Divergence errors are transported out of the
domain and damped using the mixed hyperbolic/parabolic divergence cleaning
technique by Dedner et al. (J. Comput. Phys., 175, 2002). The strength and
accuracy of the scheme are verified by a direct comparison with the eight-wave
formulation (also employing a cell-centered representation) and with the
popular constrained transport method, where magnetic field components retain a
staggered collocation inside the computational cell. Results obtained from two-
and three-dimensional test problems indicate that the newly proposed scheme is
robust, accurate and competitive with recent implementations of the constrained
transport method while being considerably easier to implement in existing hydro
codes.Comment: 31 Pages, 16 Figures Accepted for publication in Journal of
Computational Physic
An HLLC Riemann Solver for Relativistic Flows: I. Hydrodynamics
We present an extension of the HLLC approximate Riemann solver by Toro,
Spruce and Speares to the relativistic equations of fluid dynamics. The solver
retains the simplicity of the original two-wave formulation proposed by Harten,
Lax and van Leer (HLL) but it restores the missing contact wave in the solution
of the Riemann problem. The resulting numerical scheme is computationally
efficient, robust and positively conservative. The performance of the new
solver is evaluated through numerical testing in one and two dimensions.Comment: 12 pages, 12 figure
Numerical simulations of radiative magnetized Herbig-Haro jets: the influence of pre-ionization from X-rays on emission lines
We investigate supersonic, axisymmetric magnetohydrodynamic (MHD) jets with a
time-dependent injection velocity by numerical simulations with the PLUTO code.
Using a comprehensive set of parameters, we explore different jet
configurations in the attempt to construct models that can be directly compared
to observational data of microjets. In particular, we focus our attention on
the emitting properties of traveling knots and construct, at the same time,
accurate line intensity ratios and surface brightness maps. Direct comparison
of the resulting brightness and line intensity ratios distributions with
observational data of microjets shows that a closer match can be obtained only
when the jet material is pre-ionized to some degree. A very likely source for a
pre-ionized medium is photoionization by X-ray flux coming from the central
object.Comment: Accepted for publication in Ap
High-order conservative finite difference GLM-MHD schemes for cell-centered MHD
We present and compare third- as well as fifth-order accurate finite
difference schemes for the numerical solution of the compressible ideal MHD
equations in multiple spatial dimensions. The selected methods lean on four
different reconstruction techniques based on recently improved versions of the
weighted essentially non-oscillatory (WENO) schemes, monotonicity preserving
(MP) schemes as well as slope-limited polynomial reconstruction. The proposed
numerical methods are highly accurate in smooth regions of the flow, avoid loss
of accuracy in proximity of smooth extrema and provide sharp non-oscillatory
transitions at discontinuities. We suggest a numerical formulation based on a
cell-centered approach where all of the primary flow variables are discretized
at the zone center. The divergence-free condition is enforced by augmenting the
MHD equations with a generalized Lagrange multiplier yielding a mixed
hyperbolic/parabolic correction, as in Dedner et al. (J. Comput. Phys. 175
(2002) 645-673). The resulting family of schemes is robust, cost-effective and
straightforward to implement. Compared to previous existing approaches, it
completely avoids the CPU intensive workload associated with an elliptic
divergence cleaning step and the additional complexities required by staggered
mesh algorithms. Extensive numerical testing demonstrate the robustness and
reliability of the proposed framework for computations involving both smooth
and discontinuous features.Comment: 32 pages, 14 figure, submitted to Journal of Computational Physics
(Aug 7 2009
A five-wave HLL Riemann solver for relativistic MHD
We present a five-wave Riemann solver for the equations of ideal relativistic
magnetohydrodynamics. Our solver can be regarded as a relativistic extension of
the five-wave HLLD Riemann solver initially developed by Miyoshi and Kusano for
the equations of ideal MHD. The solution to the Riemann problem is approximated
by a five wave pattern, comprised of two outermost fast shocks, two rotational
discontinuities and a contact surface in the middle. The proposed scheme is
considerably more elaborate than in the classical case since the normal
velocity is no longer constant across the rotational modes. Still, proper
closure to the Rankine-Hugoniot jump conditions can be attained by solving a
nonlinear scalar equation in the total pressure variable which, for the chosen
configuration, has to be constant over the whole Riemann fan. The accuracy of
the new Riemann solver is validated against one dimensional tests and
multidimensional applications. It is shown that our new solver considerably
improves over the popular HLL solver or the recently proposed HLLC schemes.Comment: 15 pages, 19 figures. Accepted for Publication in MNRA
Modelling the Kinked Jet of the Crab Nebula
We investigate the dynamical propagation of the South-East jet from the Crab
pulsar interacting with supernova ejecta by means of three-dimensional
relativistic MHD numerical simulations with the PLUTO code.
The initial jet structure is set up from the inner regions of the Crab
Nebula.
We study the evolution of hot, relativistic hollow outflows initially
carrying a purely azimuthal magnetic field.
Our jet models are characterized by different choices of the outflow
magnetization ( parameter) and the bulk Lorentz factor ().
We show that the jet is heavily affected by the growth of current-driven kink
instabilities causing considerable deflection throughout its propagation
length.
This behavior is partially stabilized by the combined action of larger flow
velocities and/or reduced magnetic field strengths.
We find that our best jet models are characterized by relatively large values
of () and small values of .
Our results are in good agreement with the recent X-ray (\textit{Chandra})
data of the Crab Nebula South-East jet indicating that the jet changes
direction of propagation on a time scale of the order of few years.
The 3D models presented here may have important implications in the
investigation of particle acceleration in relativistic outflows.Comment: 15 pages, 20 figure
Selective large-eddy simulation of hypersonic flows. Procedure to activate the filtering in unresolved regions only (arXiv:1211.1305, submitted to Computer Physics Communications)
A new method for the localization of the regions where the turbulent fluctuations are unresolved is applied to the large-eddy simulation (LES) of a compressible turbulent jet with an initial Mach number equal to 5. The localization method used is called selective LES and is based on the exploitation of a scalar probe function f which represents the magnitude of the stretching-tilting term of the vorticity equation normalized with the enstrophy (Tordella et al. 2007). For a fully developed turbulent field of fluctuations, statistical analysis shows that the probability that f is larger than 2 is almost zero, and, for any given threshold, it is larger if the flow is under-resolved. By computing the spatial field of f in each instantaneous realization of the simulation it is possible to locate the regions where the magnitude of the normalized vortical stretching-tilting is anomalously high. The sub-grid model is then introduced into the governing equations in such regions only. The results of the selective LES simulation are compared with those of a standard LES, where the sub-grid terms are used in the whole domain. The comparison is carried out by assuming as reference field a higher resolution Euler simulation of the same jet. It is shown that the selective LES modifies the dynamic properties of the flow to a lesser extent with respect to the classical LES. In particular, the prediction of the enstrophy distribution and of the energy and density spectra are substantially improve
Linear and nonlinear evolution of current-carrying highly magnetized jets
We investigate the linear and nonlinear evolution of current-carrying jets in
a periodic configuration by means of high resolution three-dimensional
numerical simulations. The jets under consideration are strongly magnetized
with a variable pitch profile and initially in equilibrium under the action of
a force-free magnetic field. The growth of current-driven (CDI) and
Kelvin-Helmholtz (KHI) instabilities is quantified using three selected cases
corresponding to static, Alfvenic and super-Alfvenic jets.
During the early stages, we observe large-scale helical deformations of the
jet corresponding to the growth of the initially excited CDI mode. A direct
comparison between our simulation results and the analytical growth rates
obtained from linear theory reveals good agreement on condition that
high-resolution and accurate discretization algorithms are employed.
After the initial linear phase, the jet structure is significantly altered
and, while slowly-moving jets show increasing helical deformations, larger
velocity shear are violently disrupted on a few Alfven crossing time leaving a
turbulent flow structure. Overall, kinetic and magnetic energies are quickly
dissipated into heat and during the saturated regime the jet momentum is
redistributed on a larger surface area with most of the jet mass travelling at
smaller velocities. The effectiveness of this process is regulated by the onset
of KHI instabilities taking place at the jet/ambient interface and can be held
responsible for vigorous jet braking and entrainment.Comment: 14 pages, 11 figure
- …