139 research outputs found
On the time continuity of entropy solutions
We show that any entropy solution of a convection diffusion equation
in \OT belongs to
C([0,T),L^1_{Loc}(\o\O)). The proof does not use the uniqueness of the
solution
Entropy estimates for a class of schemes for the euler equations
In this paper, we derive entropy estimates for a class of schemes for the
Euler equations which present the following features: they are based on the
internal energy equation (eventually with a positive corrective term at the
righ-hand-side so as to ensure consistency) and the possible upwinding is
performed with respect to the material velocity only. The implicit-in-time
first-order upwind scheme satisfies a local entropy inequality. A
generalization of the convection term is then introduced, which allows to limit
the scheme diffusion while ensuring a weaker property: the entropy inequality
is satisfied up to a remainder term which is shown to tend to zero with the
space and time steps, if the discrete solution is controlled in L and
BV norms. The explicit upwind variant also satisfies such a weaker property, at
the price of an estimate for the velocity which could be derived from the
introduction of a new stabilization term in the momentum balance. Still for the
explicit scheme, with the above-mentioned generalization of the convection
operator, the same result only holds if the ratio of the time to the space step
tends to zero
Error estimates for a numerical approximation to the compressible barotropic Navier-Stokes equations
We present here a general method based on the investigation of the relative
energy of the system, that provides an unconditional error estimate for the
approximate solution of the barotropic Navier Stokes equations obtained by time
and space discretization. We use this methodology to derive an error estimate
for a specific DG/finite element scheme for which the convergence was proved in
[27]. This is an extended version of the paper submitted to IMAJNA
Convergence of the MAC scheme for the compressible stationary Navier-Stokes equations
We prove in this paper the convergence of the Marker and Cell (MAC) scheme
for the discretization of the steady state compressible and isentropic
Navier-Stokes equations on two or three-dimensional Cartesian grids. Existence
of a solution to the scheme is proven, followed by estimates on approximate
solutions, which yield the convergence of the approximate solutions, up to a
subsequence, and in an appropriate sense. We then prove that the limit of the
approximate solutions satisfies the mass and momentum balance equations, as
well as the equation of state, which is the main difficulty of this study
Results for a turbulent system with unbounded viscosities: weak formulations, existence of solutions, boundedness, smoothness'
We consider a circulation system arising in turbulence modelling in fluid
dynamics with unbounded eddy viscosities. Various notions of weak solutions are
considered and compared. We establish existence and regularity results. In
particular we study the boundedness of weak solutions. We also establish an
existence result for a classical solutio
Reconstruction of material losses by perimeter penalization and phase-field methods
We treat the inverse problem of determining material losses, such as
cavities, in a conducting body, by performing electrostatic measurements at the
boundary. We develop a numerical approach, based on variational methods, to
reconstruct the unknown material loss by a single boundary measurement of
current and voltage type.
The method is based on the use of phase-field functions to model the material
losses and on a perimeter-like penalization to regularize the otherwise
ill-posed problem.We justify the proposed approach by a convergence result, as
the error on the measurement goes to zero.Comment: 28 page
Improved photometry of SDSS crowded field images: Structure and dark matter content in the dwarf spheroidal galaxy Leo I
We explore how well crowded field point-source photometry can be accomplished
with SDSS data: We present a photometric pipeline based on DoPhot, and tuned
for analyzing crowded-field images from the SDSS. Using Monte Carlo simulations
we show that the completeness of source extraction is above 80% to i < 21 (AB)
and a stellar surface density of about 200 sq.amin. Hence, a specialized data
pipeline can efficiently be used for e.g. nearby resolved galaxies in SDSS
images, where the standard SDSS photometric package Photo, when applied in
normal survey mode, gives poor results. We apply our pipeline to an area of
about 3.55sq.deg. around the dwarf spheroidal galaxy (dSph) Leo I, and
construct a high S/N star-count map of Leo I via an optimized filter in
color-magnitude space (g,r,i). Although the radial surface-density profile of
the dwarf deviates from the best fit empirical King model towards outer radii,
we find no evidence for tidal debris out to a stellar surface-density of
4*10^(-3) of the central value. We determine the total luminosity of Leo I, and
model its mass using the spherical and isotropic Jeans equation. Assuming that
'mass follows light' we constrain a lower limit of the total mass of the dSph
to be (1.7+/-0.2)*10^7 Msol. Contrary, if the mass in Leo I is dominated by a
constant density dark-matter (DM) halo, then the mass within the central 12' is
(2+/-0.6)*10^8 Msol. This leads to a mass-to-light ratio of >>6 (Ic_sol), and
possibly >75 if the DM halo dominates the mass and extends further out than
12'. In summary, our results show that Leo I is a symmetric, relaxed and bound
system; this supports the idea that Leo I is a dark-matter dominated system.Comment: 13 pages, 11 figures; accepted for publication in A
Nonlinear Eigenvalues and Bifurcation Problems for Pucci's Operator
In this paper we extend existing results concerning generalized eigenvalues
of Pucci's extremal operators. In the radial case, we also give a complete
description of their spectrum, together with an equivalent of Rabinowitz's
Global Bifurcation Theorem. This allows us to solve equations involving Pucci's
operators
Simulation des écoulements à surface libre dans les turbines Pelton par une méthode hybride SPH-ALE
International audienceAn Arbitrary Lagrange Euler (ALE) description of fluid flows is used together with the meshless numerical method Smoothed Particle Hydrodynamics (SPH) to simulate free surface flows. The ALE description leads to an hybrid method that can be closely connected to the finite volume approach. It is then possible to adapt some common techniques like upwind schemes and preconditioning to remedy some of the well known drawbacks of SPH like stability and accuracy. An efficient boundary treatment based on a proper upwinding of fluid information at the boundary surface is settled. The resulting SPH-ALE numerical method is applied to simulate free surface flows encountered in Pelton turbines.La méthode numérique sans maillage Smoothed Particle Hydrodynamics (SPH) est modifiée par l'adoption d'une description Arbitrary Lagrange Euler (ALE) des écoulements fluides, dans le but de simuler des écoulements à surface libre. Le formalisme ALE conduit à une méthode numérique hybride s'apparentant sur de nombreux points à une approche volumes finis. Il est alors possible d'adapter des techniques numériques courantes comme les schémas décentrés et le préconditionnement pour résoudre certains défauts majeurs de la méthode SPH, comme la stabilité numérique ou le manque de précision. Par ailleurs, le traitement des conditions limites est réalisé par un décentrement approprié des informations fluides sur les surfaces frontières. La méthode numérique SPH-ALE résultante est appliquée à la simulation d'écoulements à surface libre tels que ceux rencontrés dans les turbines Pelton
The Resolved Structure and Dynamics of an Isolated Dwarf Galaxy: A VLT and Keck Spectroscopic Survey of WLM
We present spectroscopic data for 180 red giant branch stars in the isolated
dwarf irregular galaxy WLM. Observations of the Calcium II triplet lines in
spectra of RGB stars covering the entire galaxy were obtained with FORS2 at the
VLT and DEIMOS on Keck II allowing us to derive velocities, metallicities, and
ages for the stars. With accompanying photometric and radio data we have
measured the structural parameters of the stellar and gaseous populations over
the full galaxy. The stellar populations show an intrinsically thick
configuration with . The stellar rotation in WLM is
measured to be km s, however the ratio of rotation to
pressure support for the stars is , in contrast to the gas
whose ratio is seven times larger. This, along with the structural data and
alignment of the kinematic and photometric axes, suggests we are viewing WLM as
a highly inclined oblate spheroid. Stellar rotation curves, corrected for
asymmetric drift, are used to compute a dynamical mass of M at the half light radius (
pc). The stellar velocity dispersion increases with stellar age in a manner
consistent with giant molecular cloud and substructure interactions producing
the heating in WLM. Coupled with WLM's isolation, this suggests that the
extended vertical structure of its stellar and gaseous components and increase
in stellar velocity dispersion with age are due to internal feedback, rather
than tidally driven evolution. These represent some of the first observational
results from an isolated Local Group dwarf galaxy which can offer important
constraints on how strongly internal feedback and secular processes modulate SF
and dynamical evolution in low mass isolated objects.Comment: 14 Pages, 17 figures, 3 tables. Accepted for publication in Ap
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