Preconditioner updates applied to CFD model problems

In the present paper we concentrate on solving sequences of nonsymmetric linear systems with block structure arising from compressible flow problems. We attempt to improve the solution process by sharing part of the computational effort throughout the sequence. This is achieved by application of a cheap updating technique for preconditioners which we adapted in order to be used for our applications. Tested on three benchmark compressible flow problems, the strategy speeds up the entire computation with an acceleration being particularly pronounced in phases of instationary behavior.

Low-altitude aerial photography for optimum N fertilization of winter wheat on the North China Plain

Previous research has shown that site-specific nitrogen (N) fertilizer recommendations based on an assessment of a soil’s N supply (mineral N testing) and the crop’s N status (sap nitrate analysis) can help to decrease excessive N inputs for winter wheat on the North China Plain. However, the costs to derive such recommendations based on multiple sampling of a single field hamper the use of this approach at the on-farm level. In this study low-altitude aerial true-color photographs were used to examine the relationship between image-derived reflectance values and soil–plant data in an on-station experiment. Treatments comprised a conventional N treatment (typical farmers’ practice), an optimum N treatment (N application based on soil–plant testing) and six treatments without N (one to six cropping seasons without any N fertilizer input). Normalized intensities of the red, green and blue color bands on the photographs were highly correlated with total N concentrations, SPAD readings and stem sap nitrate of winter wheat. The results indicate the potential of aerial photography to determine in combination with on site soil–plant testing the optimum N fertilizer rate for larger fields and to thereby decrease the costs for N need assessments.

Use of digital camera to assess nitrogen status of winter wheat in the Northern China Plain

The most widely used methods to assess the nitrogen (N) status of winter wheat (Triticum aestivum L.) are the determination of plant total N by combustion, the testing of nitrate in the leaf tissue and the use of SPAD readings. However, due to their labor requirements or high costs these methods can hardly be applied to the huge wheat growing areas of the Northern China Plain. This study therefore examined an alternative method to measure the N status of wheat by using a digital camera to record the visible green light reflected from the plant canopy. The experiment was conducted near Beijing in a multi-factorial field trial with three levels of N. The intensity of green light reflected from the wheat canopy was compared to the total N concentration, to the nitrate concentration of the basal stem, and to the SPAD readings of leaves. The results show significant inverse relationships between greenness intensity, canopy total N, and SPAD readings at booting and flowering. At booting, sap nitrate <2000mgL^-1 was inversely related to greenness intensity and to sap nitrate concentration in the basal stem. At sap nitrate ~2000mgL^-1, the greenness intensity reached a plateau. At booting and flowering, significant inverse relationships between greenness intensity and shoot biomass were found. The results show the potential of the new method to assess the N status of winter wheat.

Applied mathematical problem solving, modelling, applications, and links to other subjects

The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning (applied) problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.