56,010 research outputs found
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 new multidimensional, energy-dependent two-moment transport code for neutrino-hydrodynamics
We present the new code ALCAR developed to model multidimensional, multi
energy-group neutrino transport in the context of supernovae and neutron-star
mergers. The algorithm solves the evolution equations of the 0th- and 1st-order
angular moments of the specific intensity, supplemented by an algebraic
relation for the 2nd-moment tensor to close the system. The scheme takes into
account frame-dependent effects of order O(v/c) as well as the most important
types of neutrino interactions. The transport scheme is significantly more
efficient than a multidimensional solver of the Boltzmann equation, while it is
more accurate and consistent than the flux-limited diffusion method. The
finite-volume discretization of the essentially hyperbolic system of moment
equations employs methods well-known from hydrodynamics. For the time
integration of the potentially stiff moment equations we employ a scheme in
which only the local source terms are treated implicitly, while the advection
terms are kept explicit, thereby allowing for an efficient computational
parallelization of the algorithm. We investigate various problem setups in one
and two dimensions to verify the implementation and to test the quality of the
algebraic closure scheme. In our most detailed test, we compare a fully
dynamic, one-dimensional core-collapse simulation with two published
calculations performed with well-known Boltzmann-type neutrino-hydrodynamics
codes and we find very satisfactory agreement.Comment: 30 pages, 12 figures. Revised version: several additional comments
and explanations, results remain unchanged. Accepted for publication in MNRA
LAPW vs. LMTO full-potential simulations and anharmonic dynamics of KNbO3
With the aim to get an insight in the origin of differences in the earlier
reported calculation results for KNbO3 and to test the recently proposed
implementation of the FP-LMTO method by Methfessel and van Schilfgaarde, we
perform a comparative study of the ferroelectric instability in KNbO3 by
FP-LMTO and LAPW methods. It is shown that a high precision in the description
of the charge density variations over the interstitial region in perovskite
materials is essential; the technical limitations of the accuracy of
charge-density description apparently accounted for previously reported slight
disagreement with the LAPW results. With more accurate description of the
charge density by sufficiently fine real-space grid, the results obtained by
both methods became almost identical.
In order to extract additional information (beyond the harmonic
approximation) from the total energy fit obtainable in total-energy
calculations, a scheme is proposed to solve the multidimensional vibrational
Schroedinger equation in the model of non-interacting anharmonic oscillators
via the expansion in hyperspherical harmonics.Comment: 11 pages, 2 figures, uses aipproc.sty. Presented at the Fifth
Williamsburg Workshop on First-Principles Calculations for Ferroelectric
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
- …