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