342 research outputs found
Simulation of all-scale atmospheric dynamics on unstructured meshes
The advance of massively parallel computing in the nineteen nineties and beyond encouraged finer grid intervals in numerical weather-prediction models. This has improved resolution of weather systems and enhanced the accuracy of forecasts, while setting the trend for development of unified all-scale atmospheric models. This paper first outlines the historical background to a wide range of numerical methods advanced in the process. Next, the trend is illustrated with a technical review of a versatile nonoscillatory forward-in-time finite-volume (NFTFV) approach, proven effective in simulations of atmospheric flows from small-scale dynamics to global circulations and climate. The outlined approach exploits the synergy of two specific ingredients: the MPDATA methods for the simulation of fluid flows based on the sign-preserving properties of upstream differencing; and the flexible finite-volume median-dual unstructured-mesh discretisation of the spatial differential operators comprising PDEs of atmospheric dynamics. The paper consolidates the concepts leading to a family of generalised nonhydrostatic NFTFV flow solvers that include soundproof PDEs of incompressible Boussinesq, anelastic and pseudo-incompressible systems, common in large-eddy simulation of small- and meso-scale dynamics, as well as all-scale compressible Euler equations. Such a framework naturally extends predictive skills of large-eddy simulation to the global atmosphere, providing a bottom-up alternative to the reverse approach pursued in the weather-prediction models. Theoretical considerations are substantiated by calculations attesting to the versatility and efficacy of the NFTFV approach. Some prospective developments are also discussed
Anelastic Versus Fully Compressible Turbulent Rayleigh-B\'enard Convection
Numerical simulations of turbulent Rayleigh-B\'enard convection in an ideal
gas, using either the anelastic approximation or the fully compressible
equations, are compared. Theoretically, the anelastic approximation is expected
to hold in weakly superadiabatic systems with , where denotes the superadiabatic temperature drop over the
convective layer and the bottom temperature. Using direct numerical
simulations, a systematic comparison of anelastic and fully compressible
convection is carried out. With decreasing superadiabaticity , the
fully compressible results are found to converge linearly to the anelastic
solution with larger density contrasts generally improving the match. We
conclude that in many solar and planetary applications, where the
superadiabaticity is expected to be vanishingly small, results obtained with
the anelastic approximation are in fact more accurate than fully compressible
computations, which typically fail to reach small for numerical
reasons. On the other hand, if the astrophysical system studied contains
regions, such as the solar photosphere, fully compressible
simulations have the advantage of capturing the full physics. Interestingly,
even in weakly superadiabatic regions, like the bulk of the solar convection
zone, the errors introduced by using artificially large values for
for efficiency reasons remain moderate. If quantitative errors of the order of
are acceptable in such low regions, our work suggests that
fully compressible simulations can indeed be computationally more efficient
than their anelastic counterparts.Comment: 24 pages, 9 figure
The Sun's Supergranulation
Supergranulation is a fluid-dynamical phenomenon taking place in the solar
photosphere, primarily detected in the form of a vigorous cellular flow pattern
with a typical horizontal scale of approximately 30--35~megameters, a dynamical
evolution time of 24--48~h, a strong 300--400~m/s (rms) horizontal flow
component and a much weaker 20--30~m/s vertical component. Supergranulation was
discovered more than sixty years ago, however, explaining its physical origin
and most important observational characteristics has proven extremely
challenging ever since, as a result of the intrinsic multiscale, nonlinear
dynamical complexity of the problem concurring with strong observational and
computational limitations. Key progress on this problem is now taking place
with the advent of 21st-century supercomputing resources and the availability
of global observations of the dynamics of the solar surface with high spatial
and temporal resolutions. This article provides an exhaustive review of
observational, numerical and theoretical research on supergranulation, and
discusses the current status of our understanding of its origin and dynamics,
most importantly in terms of large-scale nonlinear thermal convection, in the
light of a selection of recent findings.Comment: Major update of 2010 Liv. Rev. Sol. Phys. review. Addresses many new
theoretical, numerical and observational developments. All sections,
including discussion, revised extensively. Also includes previously
unpublished results on nonlinear dynamics of convection in large domains, and
lagrangian transport at the solar surfac
Benchmarking in a rotating annulus: a comparative experimental and numerical study of baroclinic wave dynamics
The differentially heated rotating annulus is a widely studied tabletop-size
laboratory model of the general mid-latitude atmospheric circulation. The two
most relevant factors of cyclogenesis, namely rotation and meridional
temperature gradient are quite well captured in this simple arrangement. The
radial temperature difference in the cylindrical tank and its rotation rate can
be set so that the isothermal surfaces in the bulk tilt, leading to the
formation of baroclinic waves. The signatures of these waves at the free water
surface have been analyzed via infrared thermography in a wide range of
rotation rates (keeping the radial temperature difference constant) and under
different initial conditions. In parallel to the laboratory experiments, five
groups of the MetStr\"om collaboration have conducted numerical simulations in
the same parameter regime using different approaches and solvers, and applying
different initial conditions and perturbations. The experimentally and
numerically obtained baroclinic wave patterns have been evaluated and compared
in terms of their dominant wave modes, spatio-temporal variance properties and
drift rates. Thus certain ``benchmarks'' have been created that can later be
used as test cases for atmospheric numerical model validation
The Effects of Rotation on the Evolution of Rising Omega-loops in a Stratified Model Convection Zone
We present three-dimensional MHD simulations of buoyant magnetic flux tubes
that rise through a stratified model convection zone in the presence of solar
rotation. The equations of MHD are solved in the anelastic approximation, and
the results are used to determine the effects of solar rotation on the dynamic
evolution an Omega-loop. We find that the Coriolis force significantly
suppresses the degree of fragmentation at the apex of the loop during its
ascent toward the photosphere. If the initial axial field strength of the tube
is reduced, then, in the absence of forces due to convective motions, the
degree of apex fragmentation is also reduced. We show that the Coriolis force
slows the rise of the tube, and induces a retrograde flow in both the
magnetized and unmagnetized plasma of an emerging active region.
Observationally, we predict that this flow will appear to originate at the
leading polarity, and will terminate at the trailing polarity.Comment: 25 pages, 8 figures, ApJ in pres
MAESTROeX: A Massively Parallel Low Mach Number Astrophysical Solver
We present MAESTROeX, a massively parallel solver for low Mach number
astrophysical flows. The underlying low Mach number equation set allows for
efficient, long-time integration for highly subsonic flows compared to
compressible approaches. MAESTROeX is suitable for modeling full spherical
stars as well as well as planar simulations of dynamics within localized
regions of a star, and can robustly handle several orders of magnitude of
density and pressure stratification. Previously, we have described the
development of the predecessor of MAESTROeX, called MAESTRO, in a series of
papers. Here, we present a new, greatly simplified temporal integration scheme
that retains the same order of accuracy as our previous approaches. We also
explore the use of alternative spatial mapping of the one-dimensional base
state onto the full Cartesian grid. The code leverages the new AMReX software
framework for block-structured adaptive mesh refinement (AMR) applications,
allowing for scalability to large fractions of leadership-class machines. Using
our previous studies on the convective phase of single-degenerate progenitor
models of Type Ia supernovae as a guide, we characterize the performance of the
code and validate the new algorithmic features. Like MAESTRO, MAESTROeX is
fully open source
- …