3,274 research outputs found
A New Spherical Harmonics Scheme for Multi-Dimensional Radiation Transport I: Static Matter Configurations
Recent work by McClarren & Hauck [29] suggests that the filtered spherical
harmonics method represents an efficient, robust, and accurate method for
radiation transport, at least in the two-dimensional (2D) case. We extend their
work to the three-dimensional (3D) case and find that all of the advantages of
the filtering approach identified in 2D are present also in the 3D case. We
reformulate the filter operation in a way that is independent of the timestep
and of the spatial discretization. We also explore different second- and
fourth-order filters and find that the second-order ones yield significantly
better results. Overall, our findings suggest that the filtered spherical
harmonics approach represents a very promising method for 3D radiation
transport calculations.Comment: 29 pages, 13 figures. Version matching the one in Journal of
Computational Physic
General relativistic neutrino transport using spectral methods
We present a new code, Lorene's Ghost (for Lorene's gravitational handling of
spectral transport) developed to treat the problem of neutrino transport in
supernovae with the use of spectral methods. First, we derive the expression
for the nonrelativistic Liouville operator in doubly spherical coordinates (r,
theta, phi, epsilon, Theta, Phi)$, and further its general relativistic
counterpart. We use the 3 + 1 formalism with the conformally flat approximation
for the spatial metric, to express the Liouville operator in the Eulerian
frame. Our formulation does not use any approximations when dealing with the
angular arguments (theta, phi, Theta, Phi), and is fully energy-dependent. This
approach is implemented in a spherical shell, using either Chebyshev
polynomials or Fourier series as decomposition bases. It is here restricted to
simplified collision terms (isoenergetic scattering) and to the case of a
static fluid. We finish this paper by presenting test results using basic
configurations, including general relativistic ones in the Schwarzschild
metric, in order to demonstrate the convergence properties, the conservation of
particle number and correct treatment of some general-relativistic effects of
our code. The use of spectral methods enables to run our test cases in a
six-dimensional setting on a single processor.Comment: match published versio
A Finite Element Method for Angular Discretization of the Radiation Transport Equation on Spherical Geodesic Grids
Discrete ordinate () and filtered spherical harmonics () based
schemes have been proven to be robust and accurate in solving the Boltzmann
transport equation but they have their own strengths and weaknesses in
different physical scenarios. We present a new method based on a finite element
approach in angle that combines the strengths of both methods and mitigates
their disadvantages. The angular variables are specified on a spherical
geodesic grid with functions on the sphere being represented using a finite
element basis. A positivity-preserving limiting strategy is employed to prevent
non-physical values from appearing in the solutions. The resulting method is
then compared with both and schemes using four test problems and
is found to perform well when one of the other methods fail.Comment: 24 pages, 13 figure
A realizability-preserving high-order kinetic scheme using WENO reconstruction for entropy-based moment closures of linear kinetic equations in slab geometry
We develop a high-order kinetic scheme for entropy-based moment models of a
one-dimensional linear kinetic equation in slab geometry. High-order spatial
reconstructions are achieved using the weighted essentially non-oscillatory
(WENO) method, and for time integration we use multi-step Runge-Kutta methods
which are strong stability preserving and whose stages and steps can be written
as convex combinations of forward Euler steps. We show that the moment vectors
stay in the realizable set using these time integrators along with a maximum
principle-based kinetic-level limiter, which simultaneously dampens spurious
oscillations in the numerical solutions. We present numerical results both on a
manufactured solution, where we perform convergence tests showing our scheme
converges of the expected order up to the numerical noise from the numerical
optimization, as well as on two standard benchmark problems, where we show some
of the advantages of high-order solutions and the role of the key parameter in
the limiter
"Mariage des Maillages": A new numerical approach for 3D relativistic core collapse simulations
We present a new 3D general relativistic hydrodynamics code for simulations
of stellar core collapse to a neutron star, as well as pulsations and
instabilities of rotating relativistic stars. It uses spectral methods for
solving the metric equations, assuming the conformal flatness approximation for
the three-metric. The matter equations are solved by high-resolution
shock-capturing schemes. We demonstrate that the combination of a finite
difference grid and a spectral grid can be successfully accomplished. This
"Mariage des Maillages" (French for grid wedding) approach results in high
accuracy of the metric solver and allows for fully 3D applications using
computationally affordable resources, and ensures long term numerical stability
of the evolution. We compare our new approach to two other, finite difference
based, methods to solve the metric equations. A variety of tests in 2D and 3D
is presented, involving highly perturbed neutron star spacetimes and
(axisymmetric) stellar core collapse, demonstrating the ability to handle
spacetimes with and without symmetries in strong gravity. These tests are also
employed to assess gravitational waveform extraction, which is based on the
quadrupole formula.Comment: 29 pages, 16 figures; added more information about convergence tests
and grid setu
Gravitating discs around black holes
Fluid discs and tori around black holes are discussed within different
approaches and with the emphasis on the role of disc gravity. First reviewed
are the prospects of investigating the gravitational field of a black
hole--disc system by analytical solutions of stationary, axially symmetric
Einstein's equations. Then, more detailed considerations are focused to middle
and outer parts of extended disc-like configurations where relativistic effects
are small and the Newtonian description is adequate.
Within general relativity, only a static case has been analysed in detail.
Results are often very inspiring, however, simplifying assumptions must be
imposed: ad hoc profiles of the disc density are commonly assumed and the
effects of frame-dragging and completely lacking. Astrophysical discs (e.g.
accretion discs in active galactic nuclei) typically extend far beyond the
relativistic domain and are fairly diluted. However, self-gravity is still
essential for their structure and evolution, as well as for their radiation
emission and the impact on the environment around. For example, a nuclear star
cluster in a galactic centre may bear various imprints of mutual star--disc
interactions, which can be recognised in observational properties, such as the
relation between the central mass and stellar velocity dispersion.Comment: Accepted for publication in CQG; high-resolution figures will be
available from http://www.iop.org/EJ/journal/CQ
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