An assessment of discretizations for convection-dominated convection–diffusion equations

The performance of several numerical schemes for discretizing convection-dominated convection–diffusion equations will be investigated with respect to accuracy and efficiency. Accuracy is considered in measures which are of interest in applications. The study includes an exponentially fitted finite volume scheme, the Streamline-Upwind Petrov–Galerkin (SUPG) finite element method, a spurious oscillations at layers diminishing (SOLD) finite element method, a finite element method with continuous interior penalty (CIP) stabilization, a discontinuous Galerkin (DG) finite element method, and a total variation diminishing finite element method (FEMTVD). A detailed assessment of the schemes based on the Hemker example will be presented.     

A posteriori optimization of parameters in stabilized methods for convection–diffusion problems – Part I

Stabilized finite element methods for convection-dominated problems require the choice of appropriate stabilization parameters. From numerical analysis, often only their asymptotic values are known. This paper presents a general framework for optimizing stabilization parameters with respect to the minimization of a target functional. Exemplarily, this framework is applied to the SUPG finite element method and the minimization of a residual-based error estimator, an error indicator, and a functional including the crosswind derivative of the computed solution. Benefits of the basic approach are demonstrated by means of numerical results.     

Characterization of gelatinized corn starch suspensions and resulting drop size distributions after effervescent atomization

Effervescent atomization is a promising method for economical atomization of high viscous liquids like gelatinized corn starch suspensions. The gelatinization of starch has strong influence on the viscosity of starch suspensions. It was characterized adapting a method for determination of the gelatinization degree. Rheological properties of gelatinized corn starch suspensions with concentrations ranging from 5 to 7 wt.-% were investigated. Effervescent atomization proved to be largely invariant to variations of liquid viscosity in this range. Relative gas injection pressure proved to be of highest influence on the resulting drop size distribution when varying only atomizer geometry. Applying Abel inversion to drop size measurement results depicted the opposite trend of drop sizes depending on radial position in the spray than observed by other researchers working with aqueous glass bead suspensions. Compared to conventional external mixing pneumatic atomization a reduction of atomization gas quantity of up to four times could be achieved.     

A monolithic computational approach to thermo‐structure interaction

In the present work, a monolithic solution approach for thermo‐structure interaction problems motivated by the challenging application of the behaviour of rocket nozzles is proposed. Structural and thermal fields are independently discretised via finite elements. The resulting system of equations is solved via a monolithic thermo‐structure interaction scheme, which is constructed by a block Gauss–Seidel preconditioner in combination with algebraic multigrid methods. The proposed method is tested for four numerical examples, the second Danilovskaya problem, a simplified rocket nozzle configuration, an internally loaded hollow sphere, and a fully three‐dimensional nozzle configuration of a subscale thrust chamber. Good agreement of the numerical results with results from the literature is observed. Furthermore, it is shown that the monolithic solution algorithm can handle the complete range of the parameter spectrum, whereas partitioned algorithms are limited to a certain parameter range only. Moreover, the monolithic algorithm exhibits improved efficiency and robustness compared to partitioned algorithms. Copyright © 2013 John Wiley & Sons, Ltd.     

Stable meshfree methods in fluid mechanics based on Green’s functions

Recently, stable meshfree methods for computational fluid mechanics have attracted rising interest. So far such methods mostly resort to similar strategies as already used for stabilized finite element formulations. In this study, we introduce an information theoretical interpretation of Petrov–Galerkin methods and Green’s functions. As a consequence of such an interpretation, we establish a new class of methods, the so-called information flux methods. These schemes may not be considered as stabilized methods, but rather as methods which are stable by their very nature. Using the example of convection–diffusion problems, we demonstrate these methods’ excellent stability and accuracy, both in one and higher dimensions.     

Grundwasserneubildung und ihre Ermittlung – eine Anmerkung zum Beitrag von Hölting: Modellrechnungen zur Grundwasserneubildung

Ohne Zusammenfassung Eingang des Beitrages: 23.04.97     

A review of the development and application of microalloyed medium carbon steels

Microalloyed medium-carbon steels with ferrite-pearlite microstructure were developed in the FRG in early 1972, with the primary aim of saving the cost of heat treatment. A steel with roughly 0.47% C, 0.75% Mn, 0.060% S and 0.1 % V was first used for crankshafts in cars manufactured by one of the largest European automobile companies. The effect of microalloying elements such as vanadium and niobium (niobium instead of columbium is used in this paper) in these steels and their dependence on the cooling rate from drop-forging temperatures is reviewed. Although niobium is more effective than vanadium, it leads to problems while manufacturing these steels with ~0.47% C, due to the high solution temperature of the niobium precipitates, so that preference has been given to vanadium. Further development work carried out to improve the ductility of these steels is reported. Steel compositions, which could make these steels applicable for various automobile and other engineering components, are presented.     

Kommentar II

Ohne Zusammenfassung     

ta‐C beschichtete Werkzeuge für die Trockenumformung von Aluminiumblechen

ta‐C coated tools for dry forming of aluminum sheets The suitability of ta‐C coated tool surfaces for sheet forming of aluminum alloys was examined by strip‐draw testing. It was shown that ta‐C coatings, which are known as DLC coatings with superior wear resistance are also favourable concerning the anti‐adhesive behaviour. In attempts with AlMg5Mn‐ as well as Al99Mg1‐sheet materials several hundred sheets could be formed without noticeable aluminum adhering at the ta‐C coated tool surface. Neither the coefficients of friction nor the surface qualities of the aluminum sheets worsened during the observed period. Compared with tests of uncoated tools in combination with lubricants, the dry ta‐C coated tool behaves comparable with a good lubricant. In a real clinch test with aluminum sheets the positive results from strip‐draw experiments were confirmed. Using ta‐C coated clinching stamps and no lubricants a large number of clinching processes could be performed without noticeable adhering and increase of stripping forces.     

On the demand for preventive care

This paper analyzes the demand for preventive care in an optimal control model in which utility is not contingent on the state of health and preventive measures are taken against future costs of curative care. It turns out that the demand for preventive care depends negatively on its price, and positively on the price of curative care and on the life-span. The influence of the depreciation rate on health capital is ambiguous. While the sign of the income elasticity cannot be determined in general, it may be positive if income is negatively correlated with the rate of time preference.