Hypersonic Flow over a Wedge with a Particle Flux Method

We have investigated the use of DSMC as a pseudo-Euler solver in the continuum limit by using a modification of Pullin's Equilibrium Particle Simulation Method (EPSM). EPSM is a particle-based method which is in effect the large collision rate limit of DSMC yet requires far less computational effort. We propose a modification of EPSM, the Particle Flux Method (PFM), which is intermediate between EPSM and a conventional finite volume continuum flow solver. The total mass, momentum and energy in each cell are stored. Flux particles are created at every time step and move in free flight over a short decoupling time step, carrying mass momentum and energy between cells. The new method has been demonstrated by calculating the hypersonic flow over a wedge, for which DSMC calculations are available [Bondar, Markelov, Gimelshein and Ivanov, AIAA Paper 2004-1183 (2004)]. Because of an inherent dissipation, related to the cell size and time step, the shock was thicker than that found in the DSMC calculations, but the shock location was the same. PFM is not prohibitively expensive and has some advantages over conventional continuum based flow solvers, in terms of robustness arising from its firm basis in the physics of molecular flow

True Direction Equilibrium Flux Method Applications on Rectangular 2D Meshes

In a finite volume CFD method for unsteady flow fluxes of mass, momentum and energy are exchanged between cells over a series of small time steps. The conventional approach, which we will refer to as "direction decoupling", is to estimate fluxes across interfaces in a regular array of cells by using a one-dimensional flux expression based on the component of flow velocity normal to the interface. This means that fluxes cannot be exchanged between diagonally adjacent cells since they share no cell interface, even if the local flow conditions dictate that the fluxes should flow diagonally. The direction decoupling imposed by the numerical method requires that the fluxes reach a diagonally adjacent cell in two time-steps. Here we present a 'true direction flux method', which is an updated version of Pullin's Equilibrium Flux Method (EFM) in which fluxes are derived from kinetic theory. Previous implementations of EFM in higher dimensions have used direction decoupling as described above. In this "True Direction Equilibrium Flux Method" (TDEFM) fluxes flow not only between cells sharing an interface, but also to diagonally connecting cells, or ultimately to any cell in the grid. We compare TDEFM results to those from a direction-decoupled methods using 1D fluxes calculated with EFM and a Godunov solver. The test flow is a cylindrically symmetric implosion which we solve on a two-dimensional Cartesian grid, with cell interfaces parallel to the x and y axes. Because the flow is in theory radially symmetric, any lack of radial symmetry in the solution can be used to assess the inaccuracies in the computed results. The conventional direction decoupling methods with 1D solver flux calculations (EFM or Godunov Method) produced greater asymmetries (inaccuracies) in the solution than did the new method. TDEFM requires 1% less CPU time than the direction decoupled Riemann solver and 15% more CPU time than direction decoupled EFM

Galaxy Bias and its Effects on the Baryon Acoustic Oscillations Measurements

The baryon acoustic oscillation (BAO) feature in the clustering of matter in the universe serves as a robust standard ruler and hence can be used to map the expansion history of the universe. We use high force resolution simulations to analyze the effects of galaxy bias on the measurements of the BAO signal. We apply a variety of Halo Occupation Distributions (HODs) and produce biased mass tracers to mimic different galaxy populations. We investigate whether galaxy bias changes the non-linear shifts on the acoustic scale relative to the underlying dark matter distribution presented by Seo et al (2009). For the less biased HOD models (b < 3), we do not detect any shift in the acoustic scale relative to the no-bias case, typically 0.10% \pm 0.10%. However, the most biased HOD models (b > 3) show a shift at moderate significance (0.79% \pm 0.31% for the most extreme case). We test the one-step reconstruction technique introduced by Eisenstein et al. (2007) in the case of realistic galaxy bias and shot noise. The reconstruction scheme increases the correlation between the initial and final (z = 1) density fields achieving an equivalent level of correlation at nearly twice the wavenumber after reconstruction. Reconstruction reduces the shifts and errors on the shifts. We find that after reconstruction the shifts from the galaxy cases and the dark matter case are consistent with each other and with no shift. The 1-sigma systematic errors on the distance measurements inferred from our BAO measurements with various HODs after reconstruction are about 0.07% - 0.15%.Comment: Accepted by ApJ. 21 pages, 10 figure

Emulating galaxy clustering and galaxy–galaxy lensing into the deeply non-linear regime: methodology, information, and forecasts

The combination of galaxy-galaxy lensing (GGL) with galaxy clustering is one of the most promising routes to determining the amplitude of matter clustering at low redshifts. We show that extending clustering+GGL analyses from the linear regime down to similar to 0.5 h(-1) Mpc scales increases their constraining power considerably, even after marginalizing over a flexible model of non-linear galaxy bias. Using a grid of cosmological N-body simulations, we construct a Taylor-expansion emulator that predicts the galaxy autocorrelation xi(gg)(r) and galaxy-matter cross-correlation xi(gm) (r) as a function of sigma(8), Omega(m), and halo occupation distribution (HOD) parameters, which are allowed to vary with large-scale environment to represent possible effects of galaxy assembly bias. We present forecasts for a fiducial case that corresponds to BOSS LOWZ galaxy clustering and SDSS-depth weak lensing (effective source density similar to 0.3 arcmin(-2)). Using tangential shear and projected correlation function measurements over 0.5 2 h(-1) Mpc, 4 h(-1) Mpc for gamma(t) , omega(p)). Much of this improvement comes from the non-linear clustering information, which breaks degeneracies among HOD parameters. Increasing the effective source density to 3 arcmin(-2) sharpens the constraint on sigma(8)Omega(0.6 )(m)by a further factor of two. With robust modelling into the non-linear regime, low-redshift measurements of matter clustering at the 1-per cent level with clustering+GGL alone are well within reach of current data sets such as those provided by the Dark Energy Survey.National Science Foundation Graduate Research Fellowship Program [DGE-1343012]; Department of Energy Computational Science Graduate Fellowship Program of the Office of Science; National Nuclear Security Administration in the Department of Energy [DE-FG02-97ER25308]; National Science Foundation [AST-1516997, AST-1313285, 1228509]; Department of Energy Office of Science grant [DOE-SC0013718]; Simons Foundation Investigator; Center for Cosmology and AstroParticle Physics at the Ohio State University; Faculty of Arts and Sciences Division of Science, Research Computing Group at Harvard UniversityThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

High-precision predictions for the acoustic scale in the non-linear regime

We measure shifts of the acoustic scale due to nonlinear growth and redshift distortions to a high precision using a very large volume of high-force-resolution simulations. We compare results from various sets of simulations that differ in their force, volume, and mass resolution. We find a consistency within 1.5-sigma for shift values from different simulations and derive shift alpha(z) -1 = (0.300\pm 0.015)% [D(z)/D(0)]^{2} using our fiducial set. We find a strong correlation with a non-unity slope between shifts in real space and in redshift space and a weak correlation between the initial redshift and low redshift. Density-field reconstruction not only removes the mean shifts and reduces errors on the mean, but also tightens the correlations: after reconstruction, we recover a slope of near unity for the correlation between the real and redshift space and restore a strong correlation between the low and the initial redshifts. We derive propagators and mode-coupling terms from our N-body simulations and compared with Zeldovich approximation and the shifts measured from the chi^2 fitting, respectively. We interpret the propagator and the mode-coupling term of a nonlinear density field in the context of an average and a dispersion of its complex Fourier coefficients relative to those of the linear density field; from these two terms, we derive a signal-to-noise ratio of the acoustic peak measurement. We attempt to improve our reconstruction method by implementing 2LPT and iterative operations: we obtain little improvement. The Fisher matrix estimates of uncertainty in the acoustic scale is tested using 5000 (Gpc/h)^3 of cosmological PM simulations from Takahashi et al. (2009). (abridged)Comment: Revised to match the version in print: a new figure (figure 6) is added and Section 5 (and figure 8) is revised to include more details. 19 emulated apj pages with 13 figures and 3 table

A Fast N-Body Scheme for Computational Cosmology

We provide a novel and efficient algorithm for computing accelerations in theperiodic large-N-body problem that is at the same time significantly fasterand more accurate than previous methods. Our representation of theperiodic acceleration is precisely mathematically equivalent to that determinedby Ewald summation and is computed directly as an infinite lattice sum usingthe Newtonian kernel. Retaining this kernel implies that one can(i) extend the standard open boundary numerical algorithms and(ii) harness the tremendous computational speed possessed by Graphics ProcessingUnits (GPUs) in computing Newtonian kernels straightforwardly to the periodic domain.The precise form of our direct interactions is based upon the adaptive softeninglength methodology introduced for open boundary conditions by Price and Monaghan.Furthermore, we describe a new Fast Multipole Method (FMM) that represents themultipoles and Taylor series as collections of pseudoparticles. Using thesetechniques we have computed forces to machine precision throughout the evolution ofa 1 billion particle cosmological simulation with a price/performance ratio morethan 100 times that of current numerical techniques operating at much lower accuracy

On a theory of scale types

SIGLEAvailable from Bibliothek des Instituts fuer Weltwirtschaft, ZBW, Duesternbrook Weg 120, D-24105 Kiel C 136674 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Complex shock structure in the western hot-spot of Pictor A

We have carried out simulations of supersonic light jets in order to model the features observed in optical and radio images of the western hot-spot in the radio galaxy Pictor A. We have considered jets with density ratios $\eta=10^{-2} {-} 10^{-4}$, and Mach numbers ranging between 5 and 50. From each simulation, we have generated ray-traced maps of radio surface brightness at a variety of jet inclinations, in order to study the appearance of time-dependent luminous structures in the vicinity of the western hot-spot. We compare these rendered images with observed features of Pictor A. A remarkable feature of Pictor A observations is a bar-shaped “filament” inclined almost at right angles to the inferred jet direction and extending $24''$ ($10.8~h^{-1}\,\rm kpc$) along its longest axis. The constraints of reproducing the appearance of this structure in simulations indicate that the jet of Pictor A lies nearly in the plane of the sky. The results of the simulation are also consistent with other features found in the radio image of Pictor A. This filament arises from the surging behaviour of the jet near the hot-spot; the surging is provoked by alternate compression and decompression of the jet by the turbulent backflow in the cocoon. We also examine the arguments for the jet in Pictor A being at a more acute angle to the line of sight and find that our preferred orientation is just consistent with the limits on the brightness ratio of the X-ray jet and counter-jet. We determine from our simulations, the structure function of hot-spot brightness and also the cumulative distribution of the ratio of intrinsic hot-spot brightnesses. The latter may be used to quantify the use of hot-spot ratios for the estimation of relativistic effects