An analysis of arithmetic averaging in approximate Riemann solvers with an application to steady, supercritical flows

An analysis of various arithmetic averaging procedures for approximate Riemann solvers is made with a specific emphasis on efficiency and a jump capturing property. The various alternatives discussed are intended for future work, as well as the more immediate problem of steady, supercritical free-surface flows. Numerical results are shown for two test problems.

A shock capturing scheme for steady, supercritical, free-surface flow

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

Prediction of supercritical flow in open channels

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow water equations in open channels. A linearised 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 linearised 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 problem of flow in a river whose geometry induces a region of supercritical flow.

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.

Analysis of aluminium content and iron homeostasis in nipple aspirate fluids from healthy women and breast cancer-affected patients

Aluminium is not a physiological component of the breast but has been measured recently in human breast tissues and breast cyst fluids at levels above those found in blood serum or milk. Since the presence of aluminium can lead to iron dyshomeostasis, levels of aluminium and iron-binding proteins (ferritin, transferrin) were measured in nipple aspirate fluid (NAF), a fluid present in the breast duct tree and mirroring the breast microenvironment. NAFs were collected noninvasively from healthy women (NoCancer; n = 16) and breast cancer-affected women (Cancer; n = 19), and compared with levels in serum (n = 15) and milk (n = 45) from healthy subjects. The mean level of aluminium, measured by ICP-mass spectrometry, was significantly higher in Cancer NAF (268.4 ± 28.1 μg l−1; n = 19) than in NoCancer NAF (131.3 ± 9.6 μg l−1; n = 16; P < 0.0001). The mean level of ferritin, measured through immunoassay, was also found to be higher in Cancer NAF (280.0 ± 32.3 μg l−1) than in NoCancer NAF (55.5 ± 7.2 μg l−1), and furthermore, a positive correlation was found between levels of aluminium and ferritin in the Cancer NAF (correlation coefficient R = 0.94, P < 0.001). These results may suggest a role for raised levels of aluminium and modulation of proteins that regulate iron homeostasis as biomarkers for identification of women at higher risk of developing breast cancer. The reasons for the high levels of aluminium in NAF remain unknown but possibilities include either exposure to aluminium-based antiperspirant salts in the adjacent underarm area and/or preferential accumulation of aluminium by breast tissues.

Available potential energy and exergy in stratified fluids

Lorenz’s theory of available p otential energy (APE) remains the main framework for studying the atmospheric and oceanic energy cycles. Because the APE generation rate is the volume integral of a thermodynamic efficiency times the local diabatic heating/cooling rate, APE theory is often regarded as an extension of the theory of heat engines. Available energetics in classical thermodynamics, however, usually relies on the concept of exergy, and is usually measured relative to a reference state maximising entropy at constant energy, whereas APE’s reference state minimises p otential energy at constant entropy. This review seeks to shed light on the two concepts; it covers local formulations of available energetics, alternative views of the dynamics/thermodynamics coupling, APE theory and the second law, APE production/dissipation, extensions to binary fluids, mean/eddy decomp ositions, APE in incompressible fluids, APE and irreversible turbulent mixing, and the role of mechanical forcing on APE production.

A general method for finding extremal states of Hamiltonian dynamical systems, with applications to perfect fluids

In addition to the Hamiltonian functional itself, non-canonical Hamiltonian dynamical systems generally possess integral invariants known as ‘Casimir functionals’. In the case of the Euler equations for a perfect fluid, the Casimir functionals correspond to the vortex topology, whose invariance derives from the particle-relabelling symmetry of the underlying Lagrangian equations of motion. In a recent paper, Vallis, Carnevale & Young (1989) have presented algorithms for finding steady states of the Euler equations that represent extrema of energy subject to given vortex topology, and are therefore stable. The purpose of this note is to point out a very general method for modifying any Hamiltonian dynamical system into an algorithm that is analogous to those of Vallis etal. in that it will systematically increase or decrease the energy of the system while preserving all of the Casimir invariants. By incorporating momentum into the extremization procedure, the algorithm is able to find steadily-translating as well as steady stable states. The method is applied to a variety of perfect-fluid systems, including Euler flow as well as compressible and incompressible stratified flow.

Thermodynamics/dynamics coupling in weakly compressible turbulent stratified fluids

In traditional and geophysical fluid dynamics, it is common to describe stratified turbulent fluid flows with low Mach number and small relative density variations by means of the incompressible Boussinesq approximation. Although such an approximation is often interpreted as decoupling the thermodynamics from the dynamics, this paper reviews recent results and derive new ones that show that the reality is actually more subtle and complex when diabatic effects and a nonlinear equation of state are retained. Such an analysis reveals indeed: (1) that the compressible work of expansion/contraction remains of comparable importance as the mechanical energy conversions in contrast to what is usually assumed; (2) in a Boussinesq fluid, compressible effects occur in the guise of changes in gravitational potential energy due to density changes. This makes it possible to construct a fully consistent description of the thermodynamics of incompressible fluids for an arbitrary nonlinear equation of state; (3) rigorous methods based on using the available potential energy and potential enthalpy budgets can be used to quantify the work of expansion/contraction B in steady and transient flows, which reveals that B is predominantly controlled by molecular diffusive effects, and act as a significant sink of kinetic energy.

Creep and recovery of magnetorheological fluids: experiments and simulations

A direct comparative study on the creep-recovery behavior of conventional MR fluids is carried out using magnetorheometry and particle-level simulations. Two particle concentrations are investigated (ϕ=0.05 and 0.30) at two different magnetic field strengths (53 kA•m-1 and 173 kA•m-1) in order to match the yield stresses developed in both systems for easier comparison. Simulations are mostly started with random initial structures with some additional tests of using preassembled single chains in the low concentration case. Experimental and simulation data are in good qualitative agreement. The results demonstrate three regions in the creep curves: i) In the initial viscoelastic region, the chain-like (at ϕ=0.05) or percolated three-dimensional network (at ϕ=0.30) structures fill up the gap and the average cluster size remains constant; ii) Above a critical strain of 10 %, in the retardation region, these structures begin to break and rearrange under shear. At large enough imposed stress values, they transform into thin sheet-like or thick lamellar structures, depending on the particle concentration; iii) Finally in the case of larger strain values either the viscosity diverges (at low stress values) or reaches a constant low value (at high stress values), showing a clear bifurcation behavior. For stresses below the bifurcation point the MR fluid is capable to recover the strain by a certain fraction. However, no recovery is observed for large stress values.

Bile salt composition is secondary to bile salt concentration in determining hydrocortisone and progesterone solubility in intestinal mimetic fluids.

Simulated intestinal fluids (SIFs) used to assay the solubility of orally administered drugs are typically based on a single bile salt; sodium taurocholate (STC). The aim of this study was to develop mimetic intestinal fluids with a closer similarity to physiological fluids than those reported to date by developing a mixed bile salt (MBS) system (STC, sodium glycodeoxycholate, sodium deoxycholate; 60:39:1) with different concentrations of lecithin, the preponderant intestinal phospholipid. Hydrocortisone and progesterone were used as model drugs to evaluate systematically the influence of SIF composition on solubility. Increasing total bile salt concentration from 0 to 30 mM increased hydrocortisone and progesterone solubility by 2- and ∼25-fold, respectively. Accordingly, higher solubilities were measured in the fed-state compared to the fasted-state SIFs. Progesterone showed the greatest increases in solubility in STC and MBS systems (2-7-fold) compared to hydrocortisone (no significant change; P>0.05) as lecithin concentration was increased. Overall, MBS systems gave similar solubility profiles to STC. In conclusion, the addenda of MBS and lecithin were found to be secondary to the influence of BS concentration. These data provide a foundation for the design of more bio-similar media for pivotal decision-guiding assays in drug development and quality control settings.