Evolving a puncture black hole with fixed mesh refinement

We present an algorithm for treating mesh refinement interfaces in numerical relativity. We detail the behavior of the solution near such interfaces located in the strong field regions of dynamical black hole spacetimes, with particular attention to the convergence properties of the simulations. In our applications of this technique to the evolution of puncture initial data with vanishing shift, we demonstrate that it is possible to simultaneously maintain second order convergence near the puncture and extend the outer boundary beyond 100M, thereby approaching the asymptotically flat region in which boundary condition problems are less difficult and wave extraction is meaningful.Comment: 18 pages, 12 figures. Minor changes, final PRD versio

Numerical Simulation and Wave Extraction of Binary Black Hole System.

In the first part of this work, we apply finite difference methods, specially mesh refinement techniques, in order to numerically evolve a single black hole, which is represented by the puncture initial data. We use standard second order finite differences, and the second order Iterated Crank-Nicholson integrator. We observe that, in order to obtain a second order accurate evolution we must impose second order accurate interface conditions at the refinement boundaries. We test our evolution with both the geodesic and the 1+log slicing conditions, and observe the expected results. We conclude that our mesh refinement technique generates convergent evolutions, and the puncture method behaves very well with it. The second part of this work deals with a modification of the hybrid ``Lazarus'' method for wave extraction. This method is divided in three parts: an early evolution, a set of transformations to produce perturbations over a Kerr background from the numerical data, and Teukolsky evolution. By using our evolution code (with mesh refinement) and gauges (1+log, gamma-driver, shifting-shift), we deviate from the original Lazarus approach. We used an independent implementation of the Lazarus transformations, validating the original results, and of the Teukolsky equation. We obtained results similar to the original Lazarus, both on the waveforms as well as on the negative results at later times. For instance, strong pulses that contaminate some gauge transformations, which may be explained in part by the propagating gauge modes of the 1+log slicing. Increasing the accuracy of the initial black hole evolution we seem to obtain better final results for the Kerr test case. Because of the gauge problems, we develop an approximated embedding method which approximates location of the numerical slice into the Kerr spacetime. This method is much less sensitive to the gauge perturbations. Given the difficulties of the Lazarus procedure, we decide to use the Lazarus method as a wave extraction tool. Using this embedding technique we developed the ``spacelike'' wave extraction method. Our preliminary result is consistent with the numerical waveforms for at least three cycles. Although we see some differences, it is too early to claim physical reality on them

MEDIDAS DE FLUXO DE DIÓXIDO DE CARBONO E METANO EM UM DEPÓSITO DE RESÍDUOS INSALUBRE NA AMAZÔNIA

Dumps are important anthropogenic sources of greenhouse gas emissions into the atmosphere, mostly CH4. However, few studies on the subject have been carried out in the Amazon region. Several factors affect the production and emission of dumps gas. The objective of this study was to quantify the spatial variation of CO2 and CH4 production in an Amazon dump and try to associate the relative importance of some environmental factors with the fluxes. This study was carried out in an open-air dump in the metropolitan region of Belém, where approximately 11.0 million Mg of waste was deposited in 25 years, of which 6.4 million Mg was organic. The emission rates of CH4 and CO2 from the surface of the dump were determined using the closed dynamic flux chamber technique. The study was conducted in three cells of different ages, sampled in two moments between the Amazon rainy and dry season. The Aura dump has an area of 30 ha and emits a total of 51.49 Mg CO2 ha-1 month-1 and 3.16 Mg CH4 ha-1 month-1 to the atmosphere. This results in an expressive production of 1,359,961.04 Mg CO2-e year-1, being that 58.54% is due to CH4 flux. The spatial variability in CO2 and CH4 flux is very large, especially for CH4, forming hotspots of high concentrations, and perhaps because of this, the flow has not been correlated with micrometeorological variations