Conservative upwind difference schemes for the Euler equations for real gas flows in a duct

In a recent paper [P. Glaister, Conservative upwind difference schemes for compressible flows in a Duct, Comput. Math. Appl. 56 (2008) 1787–1796] numerical schemes based on a conservative linearisation are presented for the Euler equations governing compressible flows of an ideal gas in a duct of variable cross-section, and in [P. Glaister, Conservative upwind difference schemes for compressible flows of a real gas, Comput. Math. Appl. 48 (2004) 469–480] schemes based on this philosophy are presented for real gas flows with slab symmetry. In this paper we seek to extend these ideas to encompass compressible flows of real gases in a duct. This will incorporate the handling of additional terms arising out of the variable geometry and the non-ideal nature of the gas.

An efficient flux difference splitting algorithm for unsteady duct flows of a real gas

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a real gas in a single spatial coordinate. This includes flow in a duct of variable cross-section, as well as flow with slab, cylindrical or spherical symmetry, as well as the case of an ideal gas, and can be useful when testing codes for the two-dimensional equations governing compressible flow of a real gas. The resulting scheme requires an average of the flow variables across the interface between cells, and this average is chosen to be the arithmetic mean for computational efficiency, which is in contrast to the usual “square root” averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and for a number of equations of state. The results compare favourably with the results from other schemes.

An efficient shock capturing algorithm for compressible flows in a duct of variable cross-section

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a gas in a single spatial co-ordinate. This includes flow in a duct of variable cross-section as well as flow with slab, cylindrical or spherical symmetry and can prove useful when testing codes for the two-dimensional equations governing compressible flow of a gas. The resulting scheme requires an average of the flow variables across the interface between cells and for computational efficiency this average is chosen to be the arithmetic mean, which is in contrast to the usual ‘square root’ averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and a comparison is made in the cylindrical case with results from a two-dimensional problem with no sources.

Real gas flows in a duct

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a real gas in a single spatial coordinate. This include flow in a duct of variable cross-section as well as flow with cylindrical or spherical symmetry, and can prove useful when testing codes for the two-dimensional equations governing compressible flow of a real gas. The scheme is applied with success to a problem involving the interaction of converging and diverging cylindrical shocks for four equations of state and to a problem involving the reflection of a converging shock.

DNA barcodes for Mexican Cactaceae, plants under pressure from wild collecting

DNA barcodes could be a useful tool for plant conservation. Of particular importance is the ability to identify unknown plant material, such as from customs seizures of illegally collected specimens. Mexican cacti are an example of a threatened group, under pressure because of wild collection for the xeriscaping trade and private collectors. Mexican cacti also provide a taxonomically and geographically coherent group with which to test DNA barcodes. Here, we sample the matK barcode for 528 species of Cactaceae including approximately 75% of Mexican species and test the utility of the matK region for species-level identification. We find that the matK DNA barcode can be used to identify uniquely 77% of species sampled, and 79-87% of species of particular conservation importance. However, this is far below the desired rate of 95% and there are significant issues for PCR amplification because of the variability of primer sites. Additionally, we test the nuclear ITS regions for the cactus subfamily Opuntioideae and for the genus Ariocarpus (subfamily Cactoideae). We observed higher rates of variation for ITS (86% unique for Opuntioideae sampled) but a much lower PCR success, encountering significant intra-individual polymorphism in Ariocarpus precluding the use of this marker in this taxon. We conclude that the matK region should provide useful information as a DNA barcode for Cactaceae if the problems with primers can be addressed, but matK alone is not sufficiently variable to achieve species-level identification. Additional complementary regions should be investigated as ITS is shown to be unsuitable

Collecting disability data from parents

This article describes the development and national trial of a methodology for collecting disability data directly from parents, enabling schools and local authorities to meet their obligations under the Disability Discrimination Act (DDA; 2005) to promote equality of opportunity for all children. It illustrates the complexities around collecting this information and also highlights the dangers of assuming that special educational needs (SENs) equate to disability. The parental survey revealed children with medical and mental health needs, but no SENs, who were unknown to schools. It also revealed children with a recorded SEN whose parents did not consider that they had a disability in line with the DDA definition. It identified a number of children whose disability leads to absences from school, making them vulnerable to underachievement. These findings highlight the importance of having appropriate tools with which to collect these data and developing procedures to support their effective use. We also draw attention to the contextual nature of children’s difficulties and the importance of retaining and respecting the place of subjective information. This is central to adopting a definition of disability that hinges on experience or impact.