Three-dimensional elliptic grid generation technique with application to turbomachinery cascades

Described is a numerical method for generating 3-D grids for turbomachinery computational fluid dynamic codes. The basic method is general and involves the solution of a quasi-linear elliptic partial differential equation via pointwise relaxation with a local relaxation factor. It allows specification of the grid point distribution on the boundary surfaces, the grid spacing off the boundary surfaces, and the grid orthogonality at the boundary surfaces. A geometry preprocessor constructs the grid point distributions on the boundary surfaces for general turbomachinery cascades. Representative results are shown for a C-grid and an H-grid for a turbine rotor. Two appendices serve as user's manuals for the basic solver and the geometry preprocessor

Nonlinear force-free modeling of the solar coronal magnetic field

The coronal magnetic field is an important quantity because the magnetic field dominates the structure of the solar corona. Unfortunately direct measurements of coronal magnetic fields are usually not available. The photospheric magnetic field is measured routinely with vector magnetographs. These photospheric measurements are extrapolated into the solar corona. The extrapolated coronal magnetic field depends on assumptions regarding the coronal plasma, e.g. force-freeness. Force-free means that all non-magnetic forces like pressure gradients and gravity are neglected. This approach is well justified in the solar corona due to the low plasma beta. One has to take care, however, about ambiguities, noise and non-magnetic forces in the photosphere, where the magnetic field vector is measured. Here we review different numerical methods for a nonlinear force-free coronal magnetic field extrapolation: Grad-Rubin codes, upward integration method, MHD-relaxation, optimization and the boundary element approach. We briefly discuss the main features of the different methods and concentrate mainly on recently developed new codes.Comment: 33 pages, 3 figures, Review articl

Characterization of the austenite recrystallization by comparing double deformation and stress relaxation tests

A high amount of deformation below the non-recrystallization temperature (T-nr) is a common industrial practice to achieve a good combination of toughness and strength in microalloyed steels. To combine the industrially relevant optimum combination of high productivity and product quality, an accurate knowledge of T-nr and the recrystallization kinetics is required. Although a lot of literature data is available on the recrystallization behaviour of microalloyed steels, correlations are often difficult to be made due to the effect of different experimental setups, types of analysis and test schedules that are used to obtain this data. Although this would significantly improve the knowledge about these steels, so far, no systematic comparison has been presented in literature to correlate the different techniques and methods. In this study, different hot rolling simulation techniques, testing schedules and types of analysis were used to determine the recrystallization kinetics of a microalloyed steel. On the one hand, good agreement was found between the results from different test equipment for the double deformations tests. On the other hand, stress relaxation tests showed accelerated kinetics and appeared to be less effective

Adaptive Mesh Refinement for Coupled Elliptic-Hyperbolic Systems

We present a modification to the Berger and Oliger adaptive mesh refinement algorithm designed to solve systems of coupled, non-linear, hyperbolic and elliptic partial differential equations. Such systems typically arise during constrained evolution of the field equations of general relativity. The novel aspect of this algorithm is a technique of "extrapolation and delayed solution" used to deal with the non-local nature of the solution of the elliptic equations, driven by dynamical sources, within the usual Berger and Oliger time-stepping framework. We show empirical results demonstrating the effectiveness of this technique in axisymmetric gravitational collapse simulations. We also describe several other details of the code, including truncation error estimation using a self-shadow hierarchy, and the refinement-boundary interpolation operators that are used to help suppress spurious high-frequency solution components ("noise").Comment: 31 pages, 15 figures; replaced with published versio

Configurational entropy measurements in extremely supercooled liquids that break the glass ceiling

Liquids relax extremely slowly upon approaching the glass state. One explanation is that an entropy crisis, due to the rarefaction of available states, makes it increasingly arduous to reach equilibrium in that regime. Validating this scenario is challenging, because experiments offer limited resolution, while numerical studies lag more than eight orders of magnitude behind experimentally-relevant timescales. In this work we not only close the colossal gap between experiments and simulations but manage to create in-silico configurations that have no experimental analog yet. Deploying a range of computational tools, we obtain four estimates of their configurational entropy. These measurements consistently confirm that the steep entropy decrease observed in experiments is also found in simulations, even beyond the experimental glass transition. Our numerical results thus extend the new observational window into the physics of glasses and reinforce the relevance of an entropy crisis for understanding their formation.Comment: 4+23 pages, 3+12 figures; v2: final version, with various changes made. Data relevant to this work can be accessed at http://dx.doi.org/10.7924/G8ZG6Q9

Solar Force-free Magnetic Fields

The structure and dynamics of the solar corona is dominated by the magnetic field. In most areas in the corona magnetic forces are so dominant that all non-magnetic forces like plasma pressure gradient and gravity can be neglected in the lowest order. This model assumption is called the force-free field assumption, as the Lorentz force vanishes. This can be obtained by either vanishing electric currents (leading to potential fields) or the currents are co-aligned with the magnetic field lines. First we discuss a mathematically simpler approach that the magnetic field and currents are proportional with one global constant, the so-called linear force-free field approximation. In the generic case, however, the relation between magnetic fields and electric currents is nonlinear and analytic solutions have been only found for special cases, like 1D or 2D configurations. For constructing realistic nonlinear force-free coronal magnetic field models in 3D, sophisticated numerical computations are required and boundary conditions must be obtained from measurements of the magnetic field vector in the solar photosphere. This approach is currently of large interests, as accurate measurements of the photospheric field become available from ground-based (for example SOLIS) and space-born (for example Hinode and SDO) instruments. If we can obtain accurate force-free coronal magnetic field models we can calculate the free magnetic energy in the corona, a quantity which is important for the prediction of flares and coronal mass ejections. Knowledge of the 3D structure of magnetic field lines also help us to interpret other coronal observations, e.g., EUV-images of the radiating coronal plasma.Comment: 49 pages, 11 figures, Living Reviews in Solar Physics, accepte

Alternatives to Kronig-Kramers Transformation and Testing, and Estimation of Distributions

Two alternatives to Kronig-Kramers analysis of small-signal ac immittance data are discussed and illustrated using both synthetic and experimental data. The first, a derivative method of approximating imaginary-part response from real-part data, is found to be too approximate in regions where the imaginary-part varies appreciably with frequency. The second, a distribution of relaxation-times fitting method, is shown to be valuable for testing whether a data set satisfies the Kronig-Kramers relations and so is associated with a system whose properties are time-invariant. It also is valuable for estimating real- or imaginary-part response from the other part, usually with small error. Unlike Kronig-Kramers analysis, the second method usually requires no extrapolation outside the range of the measured data. Finally, this discrete-function method also allows one to estimate the distribution of relaxation times or activation energies associated with a given set of frequency-response data. This application is described and illustrated for both synthetic and experimental data and is shown to yield good but somewhat approximate results for the estimation of continuous distributions. It is particularly valuable for identifying response regions arising from a continuous distribution and distinguishing them from those associated with discrete time-constant response