An efficient finite difference scheme for three-dimensional, non-equilibrium flows using operator splitting

An efficient finite difference scheme is presented for the inviscid terms of the three-dimensional, compressible flow equations for chemical non-equilibrium gases. This scheme represents an extension and an improvement of one proposed by the author, and includes operator splitting.

A TVD finite difference scheme with non-uniform meshes and without upstream weighting

We present a finite difference scheme, with the TVD (total variation diminishing) property, for scalar conservation laws. The scheme applies to non-uniform meshes, allowing for variable mesh spacing, and is without upstream weighting. When applied to systems of conservation laws, no scalar decomposition is required, nor are any artificial tuning parameters, and this leads to an efficient, robust algorithm.

A finite difference scheme for inviscid flows with non-eequilibrium chemistry and internal energy

A finite difference scheme is presented for the inviscid terms of the equations of compressible fluid dynamics with general non-equilibrium chemistry and internal energy.

A finite difference scheme for steady, supersonic, two-dimensional, compressible flow of real gases

A finite difference scheme is presented for the solution of the two-dimensional equations of steady, supersonic, compressible flow of real gases. The scheme incorparates numerical characteristic decomposition, is shock-capturing by design and incorporates space-marching as a result of the assumption that the flow is wholly supersonic in at least one space dimension. Results are shown for problems involving oblique hydraulic jumps and reflection from a wall.

Second order accurate upwind difference schemes for scalar conservation laws with source terms

A second order accurate, characteristic-based, finite difference scheme is developed for scalar conservation laws with source terms. The scheme is an extension of well-known second order scalar schemes for homogeneous conservation laws. Such schemes have proved immensely powerful when applied to homogeneous systems of conservation laws using flux-difference splitting. Many application areas, however, involve inhomogeneous systems of conservation laws with source terms, and the scheme presented here is applied to such systems in a subsequent paper.

Flux difference splitting for open channel flows

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow-water equations in open channels, together with an extension to two-dimensional flows. A linearized problem, analogous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearized problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second-order scheme which avoids non-physical, spurious oscillations. The scheme is applied to a one-dimensional dam-break problem, and to a problem of flow in a river whose geometry induces a region of supercritical flow. The scheme is also applied to a two-dimensional dam-break problem. The numerical results are compared with the exact solution, or other numerical results, where available.

Stability of solutions of linear difference equations with periodic coefficients

This paper represents the last technical contribution of Professor Patrick Parks before his untimely death in February 1995. The remaining authors of the paper, which was subsequently completed, wish to dedicate the article to Patrick. A frequency criterion for the stability of solutions of linear difference equations with periodic coefficients is established. The stability criterion is based on a consideration of the behaviour of a frequency hodograph with respect to the origin of coordinates in the complex plane. The formulation of this criterion does not depend on the order of the difference equation.

Floral ontogeny in Polygalaceae and its bearing on the homologies of keeled flowers in Fabales

Keeled flowers are characteristic of many species of Polygalaceae (tribe Polygaleae), in which there is often a distinctive crest located at the abaxial petal. This study of floral ontogeny across the entire family highlights potential suites of characters that relate to the evolution of keeled and crested flowers. One character suite encompasses interconnected transformations of the lateral perianth organs acting as an evolutionary module: bracteoles, lateral sepals (with delayed initiation and petaloid appearance), and lateral petals (suppressed or lost). The plastochron between initiation of the lateral sepals and that of the other sepals is relatively long in the tribe Polygaleae, in which the calyx is usually heteromorphic. By contrast, in the petal whorl, the difference between a zygomorphic and an actinomorphic corolla involves organ suppression rather than heterochrony. Four primary androecial patterns are identified in the family, and the gynoecium ranges between syncarpous‐bicarpellate and multicarpellate. Stigma diversity is based on two primary morphological types: one in which the papillate stigmatic surfaces lie close together, the other in which they are physically separated. The floral ontogeny of Polygalaceae is considered alongside comparative data available for other members of the order Fabales, and hypotheses to account for the similarities and differences between keeled flowers are discussed.

Production of pH-responsive microparticles by spray drying: investigation of experimental parameter effects on morphological and release properties

During spray drying, emphasis is placed on process optimisation to generate favourable particle morphological and flow properties. The effect of the initial feed solution composition on the drug release from the prepared microparticles is rarely considered. We investigated the effects of solvent composition, feed solution concentration and drug-loading on sodium salicylate, hydrocortisone and triamcinolone release from spray dried Eudragit L100 microparticles. Eudragit L100 is a pH-responsive polymer whose dissolution threshold is pH 6 so dissolution testing of the prepared microparticles at pH 5 and 1.2 illustrated non-polymer controlled burst release. Increasing the water content of the initial ethanolic feed solution significantly reduced hydrocortisone burst release at pH 5, as did reducing the feed solution concentration. These findings caution that changes in feed solution concentration or solvent composition not only affect particles’ morphological characteristics but can also negatively alter their drug release properties. This work also illustrate that drug-free microparticles can have different morphological properties to drug-loaded microparticles. Therefore, process optimisation needs to be carried out using drug-loaded systems. Depending on the physicochemical properties of the encapsulated API, drug-loading can affect the polymer solubility in the initial feed solution with consequent impact on microparticles morphological and release properties.