1,441 research outputs found
MAESTRO: An Adaptive Low Mach Number Hydrodynamics Algorithm for Stellar Flows
Many astrophysical phenomena are highly subsonic, requiring specialized
numerical methods suitable for long-time integration. In a series of earlier
papers we described the development of MAESTRO, a low Mach number stellar
hydrodynamics code that can be used to simulate long-time, low-speed flows that
would be prohibitively expensive to model using traditional compressible codes.
MAESTRO is based on an equation set derived using low Mach number asymptotics;
this equation set does not explicitly track acoustic waves and thus allows a
significant increase in the time step. MAESTRO is suitable for two- and
three-dimensional local atmospheric flows as well as three-dimensional
full-star flows. Here, we continue the development of MAESTRO by incorporating
adaptive mesh refinement (AMR). The primary difference between MAESTRO and
other structured grid AMR approaches for incompressible and low Mach number
flows is the presence of the time-dependent base state, whose evolution is
coupled to the evolution of the full solution. We also describe how to
incorporate the expansion of the base state for full-star flows, which involves
a novel mapping technique between the one-dimensional base state and the
Cartesian grid, as well as a number of overall improvements to the algorithm.
We examine the efficiency and accuracy of our adaptive code, and demonstrate
that it is suitable for further study of our initial scientific application,
the convective phase of Type Ia supernovae.Comment: Accepted to Astrophysical Journal Suppliment (http://iop.org). 56
pages, 15 figures
Optimal execution strategies in limit order books with general shape functions
We consider optimal execution strategies for block market orders placed in a
limit order book (LOB). We build on the resilience model proposed by Obizhaeva
and Wang (2005) but allow for a general shape of the LOB defined via a given
density function. Thus, we can allow for empirically observed LOB shapes and
obtain a nonlinear price impact of market orders. We distinguish two
possibilities for modeling the resilience of the LOB after a large market
order: the exponential recovery of the number of limit orders, i.e., of the
volume of the LOB, or the exponential recovery of the bid-ask spread. We
consider both of these resilience modes and, in each case, derive explicit
optimal execution strategies in discrete time. Applying our results to a
block-shaped LOB, we obtain a new closed-form representation for the optimal
strategy, which explicitly solves the recursive scheme given in Obizhaeva and
Wang (2005). We also provide some evidence for the robustness of optimal
strategies with respect to the choice of the shape function and the
resilience-type
Low Mach Number Modeling of Type Ia Supernovae. IV. White Dwarf Convection
We present the first three-dimensional, full-star simulations of convection
in a white dwarf preceding a Type Ia supernova, specifically the last few hours
before ignition. For these long-time calculations we use our low Mach number
hydrodynamics code, MAESTRO, which we have further developed to treat spherical
stars centered in a three-dimensional Cartesian geometry. The main change
required is a procedure to map the one-dimensional radial base state to and
from the Cartesian grid. Our models recover the dipole structure of the flow
seen in previous calculations, but our long-time integration shows that the
orientation of the dipole changes with time. Furthermore, we show the
development of gravity waves in the outer, stable portion of the star. Finally,
we evolve several calculations to the point of ignition and discuss the range
of ignition radii.Comment: 42 pages, some figures degraded to conserve space. Accepted to The
Astrophysical Journal (http://journals.iop.org/
Multidimensional Modeling of Type I X-ray Bursts. I. Two-Dimensional Convection Prior to the Outburst of a Pure Helium Accretor
We present multidimensional simulations of the early convective phase
preceding ignition in a Type I X-ray burst using the low Mach number
hydrodynamics code, MAESTRO. A low Mach number approach is necessary in order
to perform long-time integration required to study such phenomena. Using
MAESTRO, we are able to capture the expansion of the atmosphere due to
large-scale heating while capturing local compressibility effects such as those
due to reactions and thermal diffusion. We also discuss the preparation of
one-dimensional initial models and the subsequent mapping into our
multidimensional framework. Our method of initial model generation differs from
that used in previous multidimensional studies, which evolved a system through
multiple bursts in one dimension before mapping onto a multidimensional grid.
In our multidimensional simulations, we find that the resolution necessary to
properly resolve the burning layer is an order of magnitude greater than that
used in the earlier studies mentioned above. We characterize the convective
patterns that form and discuss their resulting influence on the state of the
convective region, which is important in modeling the outburst itself.Comment: 47 pages including 18 figures; submitted to ApJ; A version with
higher resolution figures can be found at
http://astro.sunysb.edu/cmalone/research/pure_he4_xrb/ms.pd
Evaluation of solar cells and arrays for potential solar power satellite applications
Proposed solar array designs and manufacturing methods are evaluated to identify options which show the greatest promise of leading up to the develpment of a cost-effective SPS solar cell array design. The key program elements which have to be accomplished as part of an SPS solar cell array development program are defined. The issues focussed on are: (1) definition of one or more designs of a candidate SPS solar array module, using results from current system studies; (2) development of the necessary manufacturing requirements for the candidate SPS solar cell arrays and an assessment of the market size, timing, and industry infrastructure needed to produce the arrays for the SPS program; (3) evaluation of current DOE, NASA and DOD photovoltaic programs to determine the impacts of recent advances in solar cell materials, array designs and manufacturing technology on the candidate SPS solar cell arrays; and (4) definition of key program elements for the development of the most promising solar cell arrays for the SPS program
Influence of adaptive mesh refinement and the hydro solver on shear-induced mass stripping in a minor-merger scenario
We compare two different codes for simulations of cosmological structure
formation to investigate the sensitivity of hydrodynamical instabilities to
numerics, in particular, the hydro solver and the application of adaptive mesh
refinement (AMR). As a simple test problem, we consider an initially spherical
gas cloud in a wind, which is an idealized model for the merger of a subcluster
or galaxy with a big cluster. Based on an entropy criterion, we calculate the
mass stripping from the subcluster as a function of time. Moreover, the
turbulent velocity field is analyzed with a multi-scale filtering technique. We
find remarkable differences between the commonly used PPM solver with
directional splitting in the Enzo code and an unsplit variant of PPM in the Nyx
code, which demonstrates that different codes can converge to systematically
different solutions even when using uniform grids. For the test case of an
unbound cloud, AMR simulations reproduce uniform-grid results for the mass
stripping quite well, although the flow realizations can differ substantially.
If the cloud is bound by a static gravitational potential, however, we find
strong sensitivity to spurious fluctuations which are induced at the cutoff
radius of the potential and amplified by the bow shock. This gives rise to
substantial deviations between uniform-grid and AMR runs performed with Enzo,
while the mass stripping in Nyx simulations of the subcluster is nearly
independent of numerical resolution and AMR. Although many factors related to
numerics are involved, our study indicates that unsplit solvers with advanced
flux limiters help to reduce grid effects and to keep numerical noise under
control, which is important for hydrodynamical instabilities and turbulent
flows.Comment: 23 pages, 18 figures, accepted for publication by Astronomy and
Computin
3D simulations of Rayleigh-Taylor mixing in core-collapse SNe with CASTRO
We present multidimensional simulations of the post-explosion hydrodynamics
in three different 15 solar mass supernova models with zero, 10^{-4} solar
metallicity, and solar metallicities. We follow the growth of the
Rayleigh-Taylor instability that mixes together the stellar layers in the wake
of the explosion. Models are initialized with spherically symmetric explosions
and perturbations are seeded by the grid. Calculations are performed in
two-dimensional axisymmetric and three-dimensional Cartesian coordinates using
the new Eulerian hydrodynamics code, CASTRO. We find as in previous work, that
Rayleigh-Taylor perturbations initially grow faster in 3D than in 2D. As the
Rayleigh-Taylor fingers interact with one another, mixing proceeds to a greater
degree in 3D than in 2D, reducing the local Atwood number and slowing the
growth rate of the instability in 3D relative to 2D. By the time mixing has
stopped, the width of the mixed region is similar in 2D and 3D simulations
provided the Rayleigh-Taylor fingers show significant interaction. Our results
imply that 2D simulations of light curves and nucleosynthesis in supernovae
(SNe) that die as red giants may capture the features of an initially
spherically symmetric explosion in far less computational time than required by
a full 3D simulation. However, capturing large departures from spherical
symmetry requires a significantly perturbed explosion. Large scale asymmetries
cannot develop through an inverse cascade of merging Rayleigh-Taylor
structures; they must arise from asymmetries in the initial explosion.Comment: 12 pages, 5 figures, ApJ accepte
Conservative Initial Mapping For Multidimensional Simulations of Stellar Explosions
Mapping one-dimensional stellar profiles onto multidimensional grids as
initial conditions for hydrodynamics calculations can lead to numerical
artifacts, one of the most severe of which is the violation of conservation
laws for physical quantities such as energy and mass. Here we introduce a
numerical scheme for mapping one-dimensional spherically-symmetric data onto
multidimensional meshes so that these physical quantities are conserved. We
validate our scheme by porting a realistic 1D Lagrangian stellar profile to the
new multidimensional Eulerian hydro code CASTRO. Our results show that all
important features in the profiles are reproduced on the new grid and that
conservation laws are enforced at all resolutions after mapping.Comment: 7 pages, 5 figures, Proceeding for Conference on Computational
Physics (CCP 2011
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