Computation of acoustic waves in a jet

A numerical treatment of acoustic waves in a jet is described. The full time dependent Euler equations are used in both linear and nonlinear formulations. The computational region of integration is artificially bounded and boundary conditions are developed to simulate outgoing waves and to enable the computational domain to be substantially restricted. Higher order methods and coordinate transformations are introduced to further reduce the number of grid points as well as to increase the efficiency of the program. Numerical results are presented for time harmonic sources as well as for sources with more complicated time dependence

Simulation of the fluctuating field of a forced jet

The fluctuating field of a jet excited by transient mass injection is simulated numerically. The model is developed by expanding the state vector as a mean state plus a fluctuating state. Nonlinear terms are not neglected and the effect of nonlinearity is studied. The results show a significant spectral broadening in the flow field due to the nonlinearity. In addition, large scale structures are broken down into smaller scales

Boundary conditions for the numerical solution of elliptic equations in exterior regions

Elliptic equations in exterior regions frequently require a boundary condition at infinity to ensure the well-posedness of the problem. Examples of practical applications include the Helmholtz equation and Laplace's equation. Computational procedures based on a direct discretization of the elliptic problem require the replacement of the condition on a finite artificial surface. Direct imposition of the condition at infinity along the finite boundary results in large errors. A sequence of boundary conditions is developed which provides increasingly accurate approximations to the problem in the infinite domain. Estimates of the error due to the finite boundary are obtained for several cases. Computations are presented which demonstrate the increased accuracy that can be obtained by the use of the higher order boundary conditions. The examples are based on a finite element formulation but finite difference methods can also be used

The numerical solution of the Helmholtz equation for wave propagation problems in underwater acoustics

The Helmholtz Equation (-delta-K(2)n(2))u=0 with a variable index of refraction, n, and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems. A numerical algorithm was developed and a computer code implemented that can effectively solve this equation in the intermediate frequency range. The equation is discretized using the finite element method, thus allowing for the modeling of complicated geometrices (including interfaces) and complicated boundary conditions. A global radiation boundary condition is imposed at the far field boundary that is exact for an arbitrary number of propagating modes. The resulting large, non-selfadjoint system of linear equations with indefinite symmetric part is solved using the preconditioned conjugate gradient method applied to the normal equations. A new preconditioner is developed based on the multigrid method. This preconditioner is vectorizable and is extremely effective over a wide range of frequencies provided the number of grid levels is reduced for large frequencies. A heuristic argument is given that indicates the superior convergence properties of this preconditioner

On accuracy conditions for the numerical computation of waves

The Helmholtz equation (Delta + K(2)n(2))u = f with a variable index of refraction n, and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems. Such problems can be solved numerically by first truncating the given unbounded domain and imposing a suitable outgoing radiation condition on an artificial boundary and then solving the resulting problem on the bounded domain by direct discretization (for example, using a finite element method). In practical applications, the mesh size h and the wave number K, are not independent but are constrained by the accuracy of the desired computation. It will be shown that the number of points per wavelength, measured by (Kh)(-1), is not sufficient to determine the accuracy of a given discretization. For example, the quantity K(3)h(2) is shown to determine the accuracy in the L(2) norm for a second-order discretization method applied to several propagation models

Stability and control of compressible flows over a surface with concave-conves curvature

The active control of spatially unstable disturbances in a laminar, two-dimensional, compressible boundary layer over a curved surface is numerically simulated. The control is effected by localized time-periodic surface heating. We consider two similar surfaces of different heights with concave-convex curvature. In one, the height is sufficiently large so that the favorable pressure gradient is sufficient to stabilize a particular disturbance. In the other case the pressure gradient induced by the curvature is destabilizing. It is shown that by using active control that the disturbance can be stabilized. The results demonstrate that the curvature induced mean pressure gradient significantly enhances the receptivity of the flow localized time-periodic surface heating and that this is a potentially viable mechanism in air

R.O.S.L.A. wisdom or folly?

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On the lack of correlation between Mg II 2796, 2803 Angstrom and Lyman alpha emission in lensed star-forming galaxies

We examine the Mg II 2796, 2803 Angstrom, Lyman alpha, and nebular line emission in five bright star-forming galaxies at 1.66<z<1.91 that have been gravitationally lensed by foreground galaxy clusters. All five galaxies show prominent Mg II emission and absorption in a P Cygni profile. We find no correlation between the equivalent widths of Mg II and Lyman alpha emission. The Mg II emission has a broader range of velocities than do the nebular emission line profiles; the Mg II emission is redshifted with respect to systemic by 100 to 200 km/s. When present, Lyman alpha is even more redshifted. The reddest components of Mg II and Lyman alpha emission have tails to 500-600 km/s, implying a strong outflow. The lack of correlation in the Mg II and Lyman alpha equivalent widths, the differing velocity profiles, and the high ratios of Mg II to nebular line fluxes together suggest that the bulk of Mg II emission does not ultimately arise as nebular line emission, but may instead be reprocessed stellar continuum emission.Comment: The Astrophysical Journal, in press. 6 pages, 2 figure

Predicting declines in physical function in persons with multiple chronic medical conditions: what we can learn from the medical problem list

BACKGROUND: Primary care physicians are caring for increasing numbers of persons with comorbid chronic illness. Longitudinal information on health outcomes associated with specific chronic conditions may be particularly relevant in caring for these populations. Our objective was to assess the effect of certain comorbid conditions on physical well being over time in a population of persons with chronic medical conditions; and to compare these effects to that of hypertension alone. METHODS: We conducted a secondary analysis of 4-year longitudinal data from the Medical Outcomes Study. A heterogeneous population of 1574 patients with either hypertension alone (referent) or one or more of the following conditions: diabetes, coronary artery disease, congestive heart failure, respiratory illness, musculoskeletal conditions and/or depression were recruited from primary and specialty (endocrinology, cardiology or mental health) practices within HMO and fee-for-service settings in three U.S. cities. We measured categorical change (worse vs. same/better) in the SF-36(R) Health Survey physical component summary score (PCS) over 4 years. We used logistic regression analysis to determine significant differences in longitudinal change in PCS between patients with hypertension alone and those with other comorbid conditions and linear regression analysis to assess the contribution of the explanatory variables. RESULTS: Specific diagnoses of CHF, diabetes and/or chronic respiratory disease; or 4 or more chronic conditions, were predictive of a clinically significant decline in PCS. CONCLUSIONS: Clinical recognition of these specific chronic conditions or 4 or more of a list of chronic conditions may provide an opportunity for proactive clinical decision making to maximize physical functioning in these populations