81 research outputs found
Stability Analysis of Galerkin/Runge-Kutta Navier-Stokes Discretisations on Unstructured Grids
This paper presents a timestep stability analysis for a class of discretisations applied to the linearised form of the Navier-Stokes equations on a 3D domain with periodic boundary conditions. Using a suitable definition of the `perturbation energy' it is shown that the energy is monotonically decreasing for both the original p.d.e. and the semi-discrete system of o.d.e.'s arising from a Galerkin discretisation on a tetrahedral grid. Using recent theoretical results concerning algebraic and generalised stability, sufficient stability limits are obtained for both global and local timesteps for fully discrete algorithms using Runge-Kutta time integration
Stochastic homogenization of the laser intensity to improve the irradiation uniformity of capsules directly driven by thousands laser beams
Illumination uniformity of a spherical capsule directly driven by laser beams has been assessed numerically. Laser facilities characterized by ND = 12, 20, 24, 32, 48 and 60 directions of irradiation with associated a single laser beam or a bundle of NB laser beams have been considered. The laser beam intensity profile is assumed super-Gaussian and the calculations take into account beam imperfections as power imbalance and pointing errors. The optimum laser intensity profile, which minimizes the root-mean-square deviation of the capsule illumination, depends on the values of the beam imperfections. Assuming that the NB beams are statistically independents is found that they provide a stochastic homogenization of the laser intensity associated to the whole bundle, reducing the errors associated to the whole bundle by the factor , which in turn improves the illumination uniformity of the capsule. Moreover, it is found that the uniformity of the irradiation is almost the same for all facilities and only depends on the total number of laser beams Ntot = ND × NB
Adaptive Mesh Refinement for Characteristic Grids
I consider techniques for Berger-Oliger adaptive mesh refinement (AMR) when
numerically solving partial differential equations with wave-like solutions,
using characteristic (double-null) grids. Such AMR algorithms are naturally
recursive, and the best-known past Berger-Oliger characteristic AMR algorithm,
that of Pretorius & Lehner (J. Comp. Phys. 198 (2004), 10), recurses on
individual "diamond" characteristic grid cells. This leads to the use of
fine-grained memory management, with individual grid cells kept in
2-dimensional linked lists at each refinement level. This complicates the
implementation and adds overhead in both space and time.
Here I describe a Berger-Oliger characteristic AMR algorithm which instead
recurses on null \emph{slices}. This algorithm is very similar to the usual
Cauchy Berger-Oliger algorithm, and uses relatively coarse-grained memory
management, allowing entire null slices to be stored in contiguous arrays in
memory. The algorithm is very efficient in both space and time.
I describe discretizations yielding both 2nd and 4th order global accuracy.
My code implementing the algorithm described here is included in the electronic
supplementary materials accompanying this paper, and is freely available to
other researchers under the terms of the GNU general public license.Comment: 37 pages, 15 figures (40 eps figure files, 8 of them color; all are
viewable ok in black-and-white), 1 mpeg movie, uses Springer-Verlag svjour3
document class, includes C++ source code. Changes from v1: revised in
response to referee comments: many references added, new figure added to
better explain the algorithm, other small changes, C++ code updated to latest
versio
Quantum singularities in a model of f(R) Gravity
The formation of a naked singularity in a model of f(R) gravity having as
source a linear electromagnetic field is considered in view of quantum
mechanics. Quantum test fields obeying the Klein-Gordon, Dirac and Maxwell
equations are used to probe the classical timelike naked singularity developed
at r=0. We prove that the spatial derivative operator of the fields fails to be
essentially self-adjoint. As a result, the classical timelike naked singularity
remains quantum mechanically singular when it is probed with quantum fields
having different spin structures.Comment: 12 pages, final version. Accepted for publication in EPJ
On the fourth-order accurate compact ADI scheme for solving the unsteady Nonlinear Coupled Burgers' Equations
The two-dimensional unsteady coupled Burgers' equations with moderate to
severe gradients, are solved numerically using higher-order accurate finite
difference schemes; namely the fourth-order accurate compact ADI scheme, and
the fourth-order accurate Du Fort Frankel scheme. The question of numerical
stability and convergence are presented. Comparisons are made between the
present schemes in terms of accuracy and computational efficiency for solving
problems with severe internal and boundary gradients. The present study shows
that the fourth-order compact ADI scheme is stable and efficient
ASTEC -- the Aarhus STellar Evolution Code
The Aarhus code is the result of a long development, starting in 1974, and
still ongoing. A novel feature is the integration of the computation of
adiabatic oscillations for specified models as part of the code. It offers
substantial flexibility in terms of microphysics and has been carefully tested
for the computation of solar models. However, considerable development is still
required in the treatment of nuclear reactions, diffusion and convective
mixing.Comment: Astrophys. Space Sci, in the pres
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