193 research outputs found
A Low Mach Number Model for Moist Atmospheric Flows
We introduce a low Mach number model for moist atmospheric flows that
accurately incorporates reversible moist processes in flows whose features of
interest occur on advective rather than acoustic time scales. Total water is
used as a prognostic variable, so that water vapor and liquid water are
diagnostically recovered as needed from an exact Clausius--Clapeyron formula
for moist thermodynamics. Low Mach number models can be computationally more
efficient than a fully compressible model, but the low Mach number formulation
introduces additional mathematical and computational complexity because of the
divergence constraint imposed on the velocity field. Here, latent heat release
is accounted for in the source term of the constraint by estimating the rate of
phase change based on the time variation of saturated water vapor subject to
the thermodynamic equilibrium constraint. We numerically assess the validity of
the low Mach number approximation for moist atmospheric flows by contrasting
the low Mach number solution to reference solutions computed with a fully
compressible formulation for a variety of test problems
Two Dimensional Simulations of Pair-Instability Supernovae
We present preliminary results from two dimensional numerical studies of pair
instability supernova (PSN). We study nuclear burning, hydrodynamic
instabilities and explosion of very massive stars. Use a new
radiation-hydrodynamics code, CASTRO.Comment: Proceedings of "The First Stars and Galaxies: Challenges for the Next
Decade", Austin, Texas, March 8-11, 2010. 2 pages, 1 figur
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
Induced Rotation in 3D Simulations of Core Collapse Supernovae: Implications for Pulsar Spins
It has been suggested that the observed rotation periods of radio pulsars
might be induced by a non-axisymmetric spiral-mode instability in the turbulent
region behind the stalled supernova bounce shock, even if the progenitor core
was not initially rotating. In this paper, using the three-dimensional AMR code
CASTRO with a realistic progenitor and equation of state and a simple neutrino
heating and cooling scheme, we present a numerical study of the evolution in 3D
of the rotational profile of a supernova core from collapse, through bounce and
shock stagnation, to delayed explosion. By the end of our simulation (420
ms after core bounce), we do not witness significant spin up of the
proto-neutron star core left behind. However, we do see the development before
explosion of strong differential rotation in the turbulent gain region between
the core and stalled shock. Shells in this region acquire high spin rates that
reach Hz, but this region contains too little mass and angular
momentum to translate, even if left behind, into rapid rotation for the full
neutron star. We find also that much of the induced angular momentum is likely
to be ejected in the explosion, and moreover that even if the optimal amount of
induced angular momentum is retained in the core, the resulting spin period is
likely to be quite modest. Nevertheless, induced periods of seconds are
possible.Comment: Accepted to the Astrophysical Journa
Pair Instability Supernovae of Very Massive Population III Stars
Numerical studies of primordial star formation suggest that the first stars
in the universe may have been very massive. Stellar models indicate that
non-rotating Population III stars with initial masses of 140-260 Msun die as
highly energetic pair-instability supernovae. We present new two-dimensional
simulations of primordial pair-instability supernovae done with the CASTRO
code. Our simulations begin at earlier times than previous multidimensional
models, at the onset of core collapse, to capture any dynamical instabilities
that may be seeded by collapse and explosive burning. Such instabilities could
enhance explosive yields by mixing hot ash with fuel, thereby accelerating
nuclear burning, and affect the spectra of the supernova by dredging up heavy
elements from greater depths in the star at early times. Our grid of models
includes both blue supergiants and red supergiants over the range in progenitor
mass expected for these events. We find that fluid instabilities driven by
oxygen and helium burning arise at the upper and lower boundaries of the oxygen
shell 20 - 100 seconds after core bounce. Instabilities driven by
burning freeze out after the SN shock exits the helium core. As the shock later
propagates through the hydrogen envelope, a strong reverse shock forms that
drives the growth of Rayleigh--Taylor instabilities. In red supergiant
progenitors, the amplitudes of these instabilities are sufficient to mix the
supernova ejecta.Comment: 42 pages, 15 figures (accepted to ApJ
Highly parallelisable simulations of time-dependent viscoplastic fluid flow simulations with structured adaptive mesh refinement
We present the extension of an efficient and highly parallelisable framework for incompressible fluid flow simulations to viscoplastic fluids. The system is governed by incompressible conservation of mass, the Cauchy momentum equation and a generalised Newtonian constitutive law. In order to simulate a wide range of viscoplastic fluids, we employ the Herschel-Bulkley model for yield-stress fluids with nonlinear stress-strain dependency above the yield limit. We utilise Papanastasiou regularisation in our algorithm to deal with the singularity in apparent viscosity. The resulting system of partial differential equations is solved using the IAMR code (Incompressible Adaptive Mesh Refinement), which uses second-order Godunov methodology for the advective terms and semi-implicit diffusion in the context of an approximate projection method to solve on adaptively refined meshes. By augmenting the IAMR code with the ability to simulate regularised Herschel-Bulkley fluids, we obtain efficient numerical software for time-dependent viscoplastic flow in three dimensions, which can be used to investigate systems not considered previously due to computational expense. We validate results from simulations using this new capability against previously published data for Bingham plastics and power-law fluids in the two-dimensional lid-driven cavity. In doing so, we expand the range of Bingham and Reynolds numbers which have been considered in the benchmark tests. Moreover, extensions to time-dependent flow of Herschel-Bulkley fluids and three spatial dimensions offer new insights into the flow of viscoplastic fluids in this test case, and we provide missing benchmark results for these extensions.Funding and technical support from BP through the BP International Centre for Advanced Materials (BP-ICAM) which made this research possible
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