Finite element method in the solution of the Euler and Navier-Stokes equations for internal flow

Finite element solutions of the Euler and Navier-Stokes equations are presented, using a simple dissipation model. The discretization is based on the weak-Galerkin weighted residual method and equal interpolation functions for all the unknowns are permitted. The nonlinearity is iterated upon using a Newton method and at each iteration the linear algebraic system is solved by a direct solver with all unknowns fully coupled. Results are presented for two-dimensional transonic inviscid flows and two- and three-dimensional incompressible viscous flows. Convergence of the algorithm is shown to be quadratic, reaching machine accuracy in very few iterations. The inviscid results demonstrate the existence of nonunique numerical solutions to the steady Euler equations.     

A discontinuous Galerkin method/HLLC solver for the Euler equations

This paper proposes a fully three‐dimensional non‐linear Euler methodology for solving aerodynamic and acoustic problems in the presence of strong shocks and rarefactions. It uses a discontinuous Galerkin method (DGM) within the element, and a Riemann solver (HLLC) at the boundaries to propagate rarefactions while preserving the entropy condition and capturing shocks with no spurious oscillations. This approach is thought to marry the best aspects of finite element and finite volume methods, achieving conservation while not requiring the solution of a large matrix. Examples in which shock and rarefaction waves are well captured are presented and the propagation of acoustic pulses is well demonstrated. Copyright © 2003 John Wiley & Sons, Ltd.     

A sequential radiochemical procedure for isotopic analysis of uranium and thorium in soil

A sequential radiochemical procedure for isotopic analysis of uranium and thorium in soil has been developed. Analysis involves total dissolution of the samples to allow equilibration of the natural isotopes with added tracers, followed by radiochemical separation using anion exchange chromatography (BioRad AG 1–X8). Further separation and purification is performed employing solvent extraction techniques. Finally, the U and Th fractions are co-precipitated with lanthanum and cerium fluoride, respectively, and quantified by alpha-particle spectrometry. Overall chemical yields range from 60 to 90%. Under normal operating conditions and present counting set up, the minimum detectable concentration (MDC) is approximately 2 Bq/kg for soil samples. This is based on one gram aliquot of sample, 80% chemical yield, and 1000 minute counting with a detector having about 15% counting efficiency. The procedure has been successfully tested with Standard Reference Materials. Various soil samples were analyzed with high chemical yields and fine quality of alpha-spectra. Decontamination factor studies were performed to determine the extent of the carry over of²¹⁰Po,²²⁵Ac,²²⁶Ra, and²²⁹Th into U fraction and²¹⁰Po,²²⁵Ac,²²⁶Ra, and²³²U into Th fraction.     

Supplier quality improvement: The value of information under uncertainty

We consider supplier development decisions for prime manufacturers with extensive supply bases producing complex, highly engineered products. We propose a novel modelling approach to support supply chain managers decide the optimal level of investment to improve quality performance under uncertainty. We develop a Poisson–Gamma model within a Bayesian framework, representing both the epistemic and aleatory uncertainties in non-conformance rates. Estimates are obtained to value a supplier quality improvement activity and assess if it is worth gaining more information to reduce epistemic uncertainty. The theoretical properties of our model provide new insights about the relationship between the degree of epistemic uncertainty, the effectiveness of development programmes, and the levels of investment. We find that the optimal level of investment does not have a monotonic relationship with the rate of effectiveness. If investment is deferred until epistemic uncertainty is removed then the expected optimal investment monotonically decreases as prior variance increases but only if the prior mean is above a critical threshold. We develop methods to facilitate practical application of the model to industrial decisions by a) enabling use of the model with typical data available to major companies and b) developing computationally efficient approximations that can be implemented easily. Application to a real industry context illustrates the use of the model to support practical planning decisions to learn more about supplier quality and to invest in improving supplier capability.     

Decoherence of anyonic charge in interferometry measurements

We examine interferometric measurements of the topological charge of (non-Abelian) anyons. The target's topological charge is measured from its effect on the interference of probe particles sent through the interferometer. We find that superpositions of distinct anyonic charges a and a' in the target decohere (exponentially in the number of probes particles used) when the probes have nontrivial monodromy with the charges that may be fused with a to give a'.     

A 3D mesh deformation technique for irregular in‐flight ice accretion

Aircraft holding around busy airports may be requested to sustain as much as 45 min of icing before landing or being diverted to another airport. In this paper, a three‐dimensional mesh deformation scheme, based on a structural frame analogy, is proposed for the numerical simulation of ice accretion during extended exposure to adverse weather conditions. The goal is to provide an approach that is robust and efficient enough to delay or altogether avoid re‐meshing while preserving (enforcing) nearly orthogonal elements at the highly distorted ice surface. Robustness is achieved by suitably modifying the axial and torsional stiffness components of the frame elements in order to handle large and irregular grid displacements typical of in‐flight icing. Computational efficiency is obtained by applying the mesh displacement to an automatically selected small subset of the entire computational domain. The methodology is validated first in the case of deformations typical of fluid‐structure interaction problems, including wing bending, a helicopter rotor in forward flight, and the twisting of a high‐lift wing configuration. The approach is then assessed for aero‐icing on two swept wings and compared against experimental measurements where available. Copyright © 2015 John Wiley & Sons, Ltd.     

Finite element stream function-vorticity solutions of the incompressible Navier-Stokes equations

The incompressible, two-dimensional Navier-Stokes equations are solved by the finite element method (FEM) using a novel stream function/vorticity formulation. The no-slip solid walls boundary condition is applied by taking advantage of the simple implementation of natural boundary conditions in the FEM, eliminating the need for an iterative evaluation of wall vorticity formulae. In addition, with the proper choice of elements, a stable scheme is constructed allowing convergence to be achieved for all Reynolds numbers, from creeping to inviscid flow, without the traditional need for upwinding and its associated false diffusion. Solutions are presented for a variety of geometries.     

Modeling and optimizing of sonochemical degradation of Basic Blue 41 via response surface methodology

The nanocatalyst-assisted sonodegradation of Basic Blue 41 (BB41) dye in aqueous medium was modeled and optimized using response surface method (RSM) based on Box-Behnken design. The studied variables included pH, initial dye concentration, H₂O₂ concentration and sonolysis time while each factor varied at three levels: Low level (−1), Medium level (0) and High level (+1). The ultrasound -assisted degradation was well described by developing quadratic model with correlation value squared (R²) of 0.9114. Factor effects along with interaction effects were evaluated. The graphical optimization step was conducted to achieve the best experimental condition in dye removal. pH, H₂O₂ concentration and initial dye concentration of the reaction were investigated. It was recognized that at lower pH values the dye removal rate decreased. However, dye removal rate increased (82.5%) by increasing the concentration of H₂O₂ and by lowering the initial dye concentration.      

A new three-component reaction: green synthesis of novel isoindolo[2,1-a]quinazoline derivatives as potent inhibitors of TNF-α

Concurrent construction of five and six membered fused N-heretocyclic ring was achieved via a conceptually new three-component reaction affording 6,6a-dihydroisoindolo[2,1-a]quinazoline-5,11-diones as novel inhibitors of TNF-αin vitro. This represents one of the few examples of direct TNF-α inhibition by small molecules.