1,075 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
A Hybrid Adaptive Low-Mach-Number/Compressible Method: Euler Equations
Flows in which the primary features of interest do not rely on high-frequency
acoustic effects, but in which long-wavelength acoustics play a nontrivial
role, present a computational challenge. Integrating the entire domain with
low-Mach-number methods would remove all acoustic wave propagation, while
integrating the entire domain with the fully compressible equations can in some
cases be prohibitively expensive due to the CFL time step constraint. For
example, simulation of thermoacoustic instabilities might require fine
resolution of the fluid/chemistry interaction but not require fine resolution
of acoustic effects, yet one does not want to neglect the long-wavelength wave
propagation and its interaction with the larger domain. The present paper
introduces a new multi-level hybrid algorithm to address these types of
phenomena. In this new approach, the fully compressible Euler equations are
solved on the entire domain, potentially with local refinement, while their
low-Mach-number counterparts are solved on subregions of the domain with higher
spatial resolution. The finest of the compressible levels communicates
inhomogeneous divergence constraints to the coarsest of the low-Mach-number
levels, allowing the low-Mach-number levels to retain the long-wavelength
acoustics. The performance of the hybrid method is shown for a series of test
cases, including results from a simulation of the aeroacoustic propagation
generated from a Kelvin-Helmholtz instability in low-Mach-number mixing layers.
It is demonstrated that compared to a purely compressible approach, the hybrid
method allows time-steps two orders of magnitude larger at the finest level,
leading to an overall reduction of the computational time by a factor of 8
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
A Numerical Study of Methods for Moist Atmospheric Flows: Compressible Equations
We investigate two common numerical techniques for integrating reversible
moist processes in atmospheric flows in the context of solving the fully
compressible Euler equations. The first is a one-step, coupled technique based
on using appropriate invariant variables such that terms resulting from phase
change are eliminated in the governing equations. In the second approach, which
is a two-step scheme, separate transport equations for liquid water and vapor
water are used, and no conversion between water vapor and liquid water is
allowed in the first step, while in the second step a saturation adjustment
procedure is performed that correctly allocates the water into its two phases
based on the Clausius-Clapeyron formula. The numerical techniques we describe
are first validated by comparing to a well-established benchmark problem.
Particular attention is then paid to the effect of changing the time scale at
which the moist variables are adjusted to the saturation requirements in two
different variations of the two-step scheme. This study is motivated by the
fact that when acoustic modes are integrated separately in time (neglecting
phase change related phenomena), or when sound-proof equations are integrated,
the time scale for imposing saturation adjustment is typically much larger than
the numerical one related to the acoustics
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
Low Mach Number Modeling of Type Ia Supernovae
We introduce a low Mach number equation set for the large-scale numerical
simulation of carbon-oxygen white dwarfs experiencing a thermonuclear
deflagration. Since most of the interesting physics in a Type Ia supernova
transpires at Mach numbers from 0.01 to 0.1, such an approach enables both a
considerable increase in accuracy and savings in computer time compared with
frequently used compressible codes. Our equation set is derived from the fully
compressible equations using low Mach number asymptotics, but without any
restriction on the size of perturbations in density or temperature. Comparisons
with simulations that use the fully compressible equations validate the low
Mach number model in regimes where both are applicable. Comparisons to
simulations based on the more traditional anelastic approximation also
demonstrate the agreement of these models in the regime for which the anelastic
approximation is valid. For low Mach number flows with potentially finite
amplitude variations in density and temperature, the low Mach number model
overcomes the limitations of each of the more traditional models and can serve
as the basis for an accurate and efficient simulation tool.Comment: Accepted for publication in the Astrophysical Journal 31 pages, 5
figures (some figures degraded in quality to conserve space
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