A comparison of conservative upwind difference schemes for the Euler equations

Numerical results are presented and compared for three conservative upwind difference schemes for the Euler equations when applied to two standard test problems. This includes consideration of the effect of treating part of the flux balance as a source, and a comparison of different averaging of the flow variables. Two of the schemes are also shown to be equivalent in their implementation, while being different in construction and having different approximate Jacobians. (C) 2006 Elsevier Ltd. All rights reserved.

Upwind solution of singular differential equations arising from steady channel flows

We study ordinary nonlinear singular differential equations which arise from steady conservation laws with source terms. An example of steady conservation laws which leads to those scalar equations is the Saint–Venant equations. The numerical solution of these scalar equations is sought by using the ideas of upwinding and discretisation of source terms. Both the Engquist–Osher scheme and the Roe scheme are used with different strategies for discretising the source terms.

How to save a bad element with weak boundary conditions

The P-1-P-1 finite element pair is known to allow the existence of spurious pressure (surface elevation) modes for the shallow water equations and to be unstable for mixed formulations. We show that this behavior is strongly influenced by the strong or the weak enforcement of the impermeability boundary conditions. A numerical analysis of the Stommel model is performed for both P-1-P-1 and P-1(NC)-P-1 mixed formulations. Steady and transient test cases are considered. We observe that the P-1-P-1 element exhibits stable discrete solutions with weak boundary conditions or with fully unstructured meshes. (c) 2005 Elsevier Ltd. All rights reserved.

Generic systolic array for genetic algorithms

The authors present a systolic design for a simple GA mechanism which provides high throughput and unidirectional pipelining by exploiting the inherent parallelism in the genetic operators. The design computes in O(N+G) time steps using O(N2) cells where N is the population size and G is the chromosome length. The area of the device is independent of the chromosome length and so can be easily scaled by replicating the arrays or by employing fine-grain migration. The array is generic in the sense that it does not rely on the fitness function and can be used as an accelerator for any GA application using uniform crossover between pairs of chromosomes. The design can also be used in hybrid systems as an add-on to complement existing designs and methods for fitness function acceleration and island-style population management

Quality of medicines stored together in multi-compartment compliance aids

Background and Objective: Dispensing medicines into compliance aids is a common practice in pharmacy contrary to manufacturers’ advice and studies have shown the appearance of light-sensitive tablets is compromised by such storage; we previously found evidence of reduced bioavailability at elevated temperature and humidity. Our objective was to examine the physicochemical stability of two generic atenolol tablets in different compliance aids and with aspirin co-storage at room temperature and at 40 °C/75% relative humidity. Methods: The physicochemical stability of atenolol tablets was evaluated after 28 days of storage and compared with controls by examining visual appearance, weight, disintegration, dissolution, friability and hardness to accepted standards and using a previously validated HPLC method for chemical assay. Results and Discussion: The response to storage was brand-dependent and not straightforward. With one make of atenolol (Alpharma), storage in compliance aids even at room temperature impacted on physical stability, reducing tablet hardness, with storage in Dosett® exerting a greater impact than storage in Medidos® (t-test P < 0·001). Co-storage at elevated temperature and humidity also impacted on the appearance of non-coated aspirin tablets (Angette™). The chemical stability of atenolol was not affected and we did not find evidence of changes to bioavailability with either make. Certainly data for one atenolol make (CP Pharmaceuticals) co-stored with aspirin (Angette™ and Nu-Seals) in both compliance aids at room temperature provided evidence of short-term stability. But medicines are dispensed into compliance aids in multi-factorial ways so our study highlights not only the lack of evidence but also a realization that evidence to support real practice may not be accomplished through research. Conclusion: Reassuring practitioners of the continued stability of medicines in compliance aids under the countless condition in which they are dispensed in practice may requires a different approach involving medical device regulators and more definitive professional guidance.

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.