A non‐linear and non‐local boundary condition for a diffusion equation in petroleum engineering

This article deals with a boundary value problem for Laplace equation with a non‐linear and non‐local boundary condition. This problem comes from petroleum engineering and is used to obtain an estimation of well productivity. The non‐linear and non‐local boundary condition is written on the well boundary. On the outer reservoir boundaries, we have both Dirichlet and Neumann conditions. In this paper, we prove the existence and uniqueness of a solution to this problem. The existence is proved by Schauder theorem and the uniqueness is obtained under more restricted conditions, when the involved operator is a contraction. Copyright © 2005 John Wiley & Sons, Ltd.     

Rotational analysis ofA 1Π-X 1Σ+ bands of P14N and P15N: Perturbatio studies in theA 1Π state

The ultraviolet band systemsA ¹Π-X ¹Σ⁺ of P¹⁴N and P¹⁵N were excited in an electrodeless tube containing traces of phosphorus specpure nitrogen and neon using a microwave discharge (2450 MHz). Bands of the isotopic species, P¹⁵N, were obtained using¹⁵N₂ enriched to 95.5%. Rotational analyses of eleven bands of P¹⁴N and sixteen bands of P¹⁵N were carried out. Three perturbing statese ³Σ⁻,d ³Δ andb ³Π, arising from the lower valence configurations were identified from the observed perturbations in thev′=0–4 levels of theA ¹Π state. Deperturbation studies led to the determination of molecular constants of the perturbing states. Vibrational assignments of the perturbing states were made from isotope shift studies.     

Detecting instabilities in flows of viscoelastic fluids

There is a growing interest in developing numerical tools to investigate the onset of physical instabilities observed in experiments involving viscoelastic flows, which is a difficult and challenging task as the simulations are very sensitive to numerical instabilities. Following a recent linear stability analysis carried out in order to better understand qualitatively the origin of numerical instabilities occurring in the simulation of flows viscoelastic fluids, the present paper considers a possible extension for more complex flows. This promising method could be applied to track instabilities in complex (i.e. essentially non‐parallel) flows. In addition, results related to transient growth mechanism indicate that it might be responsible for the development of numerical instabilities in the simulation of viscoelastic fluids. Copyright © 2003 John Wiley & Sons, Ltd.     

Crystal and Molecular Structure of <Emphasis Type="Italic">Bis</Emphasis>(2,3-pentamethylene-3,4-dihydro-4-oxoquinazolinium) Tetrachlorocuprate(II) Sesquihydrate

The structure of bis-(2,3-pentamethylene-3,4-dihydro-4-oxoquinazolinium) tetrachlorocuprate (II) sesquihydrate, (C₁₃H₁₅N₂O)₂[CuCl₄]·1.5H₂O, was determined by single crystal X-ray diffraction. In contrast to the previously studied analogs, the compound contains crystallization water molecules.Original Russian Text Copyright © 2004 by K. K. Turgunov, B. Tashkhodzhaev, L. V. Molchanov, and Kh. M. Shakhidoyatov__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 5, pp. 955–959, September–October, 2004.     

Synthesis and conformational investigation of tetrapeptide analogues of the fragment B23-B26 of insulin

Tetrapeptides containing one of a set of four different α,α-dialkyl glycines at the C-terminus were synthesized by conventional methods in solution and their conformational behavior investigated by ¹H NMR spectroscopy in connection with molecular mechanics calculations. The results were consistent with conformations stabilized by a γ-turn in the case of compounds with alkyl groups larger than methyl, while the corresponding Aib derivative did not exhibit intramolecular hydrogen bonding.     

An improved numerical simulator for multiphase flow in porous media

In basin modelling the thermodynamics of a multicomponent multiphase fluid flux are computationally too expensive when derived from an equation of state and the Gibbs equality constraints. In this article we present a novel implicit molar mass formulation technique using binary mixture thermodynamics. The two proposed solution methods, with and without cross derivative terms between components, are based on a preconditioned Newton‐GMRES scheme for each time‐step with analytical computation of the derivatives. These new algorithms reduce significantly the numerical effort for the computation of the molar masses, and we illustrate the behavior of these methods with numerical computations. Copyright © 2004 John Wiley & Sons Ltd.     

Assessment of two‐equation turbulence modelling for high Reynolds number hydrofoil flows

This paper presents an evaluation of the capability of turbulence models available in the commercial CFD code FLUENT 6.0 for their application to hydrofoil turbulent boundary layer separation flow at high Reynolds numbers. Four widely applied two‐equation RANS turbulence models were assessed through comparison with experimental data at Reynolds numbers of 8.284×106 and 1.657×107. They were the standard k–εmodel, the realizable k–εmodel, the standard k–ωmodel and the shear‐stress‐transport (SST) k–ωmodel. It has found that the realizable k–εturbulence model used with enhanced wall functions and near‐wall modelling techniques, consistently provides superior performance in predicting the flow characteristics around the hydrofoil. Copyright © 2004 John Wiley & Sons, Ltd.     

High‐order accurate numerical solutions of incompressible flows with the artificial compressibility method

A high‐order accurate, finite‐difference method for the numerical solution of incompressible flows is presented. This method is based on the artificial compressibility formulation of the incompressible Navier–Stokes equations. Fourth‐ or sixth‐order accurate discretizations of the metric terms and the convective fluxes are obtained using compact, centred schemes. The viscous terms are also discretized using fourth‐order accurate, centred finite differences. Implicit time marching is performed for both steady‐state and time‐accurate numerical solutions. High‐order, spectral‐type, low‐pass, compact filters are used to regularize the numerical solution and remove spurious modes arising from unresolved scales, non‐linearities, and inaccuracies in the application of boundary conditions. The accuracy and efficiency of the proposed method is demonstrated for test problems. Copyright © 2004 John Wiley & Sons, Ltd.     

Free boundary viscous flows at micro and mesolevel during liquid composites moulding process

Numerical simulation aspects, related to low Reynolds number free boundary viscous flows at micro and mesolevel during the resin impregnation stage of the liquid composite moulding process (LCM), are presented in this article. A free boundary program (FBP), developed by the authors, is used to track the movement of the resin front accurately by accounting for the surface tension effects at the boundary. Issues related to the global and local mass conservation (GMC and LMC) are identified and discussed. Unsuitable conditions for LMC and consequently GMC are uncovered at low capillary numbers, and hence a strategy for the numerical simulation of such flows is suggested. FBP encompasses a set of subroutines that are linked to modules in ANSYS. FBP can capture the void formation dynamics based on the analysis developed. We present resin impregnation dynamics in two dimensions. Extension to three dimensions is a subject for further research. Several examples are shown and efficiency of different stabilization techniques are compared. Copyright © 2004 John Wiley & Sons, Ltd.     

A subdomain boundary element method for high‐Reynolds laminar flow using stream function‐vorticity formulation

The paper presents a new formulation of the integral boundary element method (BEM) using subdomain technique. A continuous approximation of the function and the function derivative in the direction normal to the boundary element (further ‘normal flux’) is introduced for solving the general form of a parabolic diffusion‐convective equation. Double nodes for normal flux approximation are used. The gradient continuity is required at the interior subdomain corners where compatibility and equilibrium interface conditions are prescribed. The obtained system matrix with more equations than unknowns is solved using the fast iterative linear least squares based solver. The robustness and stability of the developed formulation is shown on the cases of a backward‐facing step flow and a square‐driven cavity flow up to the Reynolds number value 50 000. Copyright © 2004 John Wiley & Sons, Ltd.