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

A Spitzer/IRAC Census of the Asymptotic Giant Branch Populations in Local Group Dwarfs. I. WLM

We present Spitzer/IRAC observations at 3.6 and 4.5 microns along with optical data from the Local Group Galaxies Survey to investigate the evolved stellar population of the Local Group dwarf irregular galaxy WLM. These observations provide a nearly complete census of the asymptotic giant branch (AGB) stars. We find 39% of the infrared-detected AGB stars are not detected in the optical data, even though our 50% completeness limit is three magnitudes fainter than the red giant branch tip. An additional 4% of the infrared-detected AGBs are misidentified in the optical, presumably due to reddening by circumstellar dust. We also compare our results with those of a narrow-band optical carbon star survey of WLM, and find the latter study sensitive to only 18% of the total AGB population. We detect objects with infrared fluxes consistent with them being mass-losing AGB stars, and derive a present day total mass-loss rate from the AGB stars of 0.7-2.4 x 10^(-3) solar masses per year. The distribution of mass-loss rates and bolometric luminosities of AGBs and red supergiants are very similar to those in the LMC and SMC and the empirical maximum mass-loss rate observed in the LMC and SMC is in excellent agreement with our WLM data.Comment: Accepted by ApJ, 34 pages, 13 figures, version with high-resolution figures available at: http://webusers.astro.umn.edu/~djackson

Problems involving pp-Laplacian type equations and measures

summary:In this paper I discuss two questions on $p$-Laplacian type operators: I characterize sets that are removable for Hölder continuous solutions and then discuss the problem of existence and uniqueness of solutions to $-\div (|\nabla u|^{p-2}\nabla u)=\mu$ with zero boundary values; here $\mu$ is a Radon measure. The joining link between the problems is the use of equations involving measures

Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data

We consider the differential problem {A(u) = mu in Omega, u = 0 on partial derivative Omega, (*) where Omega is a bounded, open subset of R(N), N greater than or equal to 2, A is a monotone operator acting on W-0(1,p)(Omega), p > 1, and mu is a Radon measure on Omega that does not charge the sets of zero p-capacity. We prove a decomposition theorem for these measures (more precisely, as the sum of a function in L(1)(Omega) and of a measure in W--1,W-p'(Omega)), and an existence and uniqueness result for the so-called entropy solutions of (*)