On pressure separation algorithms (PSepA) for improving the accuracy of incompressible flow simulations

We investigate a special technique called ‘pressure separation algorithm’ (PSepA) (see Applied Mathematics and Computation 2005; 165 :275–290 for an introduction) that is able to significantly improve the accuracy of incompressible flow simulations for problems with large pressure gradients. In our numerical studies with the computational fluid dynamics package FEATFLOW ( www.featflow.de ), we mainly focus on low‐order Stokes elements with nonconforming finite element approximations for the velocity and piecewise constant pressure functions. However, preliminary numerical tests show that this advantageous behavior can also be obtained for higher‐order discretizations, for instance, with Q₂/P₁ finite elements. We analyze the application of this simple, but very efficient, algorithm to several stationary and nonstationary benchmark configurations in 2D and 3D (driven cavity and flow around obstacles), and we also demonstrate its effect to spurious velocities in multiphase flow simulations (‘static bubble’ configuration) if combined with edge‐oriented, resp., interior penalty finite element method stabilization techniques. Copyright © 2008 John Wiley & Sons, Ltd.     

On the Ising Model with Strongly Anisotropic External Field

In this paper we analyze the equilibrium phase diagram of the two-dimensional ferromagnetic n.n. Ising model when the external field takes alternating signs on different rows. We show that some of the zero-temperature coexistence lines disappear at every positive sufficiently small temperature, whereas one (and only one) of them persists for sufficiently low temperature.     

Dendriform equations

We investigate solutions for a particular class of linear equations in dendriform algebras. Motivations as well as several applications are provided. The latter follow naturally from the intimate link between dendriform algebras and Rota–Baxter operators, e.g. the Riemann integral map or Jackson's q-integral.     

Matrix and vector models in the strong coupling limit

We consider matrix and vector models in the large-N limit: we study N × N matrices and vectors with N² components. In the case of a zero-dimensional model (D = 0), we prove that in the strong coupling limit (g → ∞), the partition functions of the two models coincide up to a coefficient. This also holds for D = 1. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 2, pp. 236–243, May, 2008.     

Numerical study of magnetohydrodynamic laminar flow separation in a channel with smooth expansion

The flow of an electrically conducting incompressible viscous fluid in a plane channel with smooth expansion in the presence of a uniform transverse magnetic field has been analysed. A solution technique for the governing magnetohydrodynamic equations in primitive variable formulation has been developed. A co‐ordinate transformation has been employed to map the infinite irregular domain into a finite regular computational domain. The governing equations are discretized using finite‐difference approximations in staggered grid. Pressure Poisson equation and pressure correction formulae are derived and solved numerically. It is found that with increase in the magnetic field, the size of the flow separation zone diminishes and for sufficiently large magnetic field, the separation zone disappears completely. The peak u‐velocity decreases with increase in the magnetic field. It is also found that the asymmetric flow in a symmetric geometry, which occurs at moderate Reynolds numbers, becomes symmetric with sufficient increase in the transverse magnetic field. Thus, a transverse magnetic field of suitable strength has a stabilizing effect in controlling flow separation, as also in delaying the transition to turbulence. Copyright © 2008 John Wiley & Sons, Ltd.     

Degenerate cascade fluorescence: Optical spectral-line narrowing via a single microwave cavity

For a three-level atom, two nondegenerate(even microwave and optical) electric dipole transitions are usually allowed; for either of these, the fluorescence spectra are well-described in terms of spontaneous transitions from a triplet of dressed sublevels to an adjacent lower-lying triplet. When the three dressed sublevels are equally spaced from each other, a remarkable feature known as degenerate cascade fluorescence takes place, which displays a five-peaked structure. We show that a single cavity can make all the spectral lines extremely narrow, whether they arise from cavity-coupled or cavity-free transitions. This effect is based on intrinsic cascade lasing feedback and makes it possible to use a single microwave cavity(even a bad cavity) to narrow the spectral lines in the optical frequency regime.     

Le jet libre immergé d'un fluide viscoélastique

Résumé Les auteurs étudient le jet libre laminaire bidimensionnel d'un fluide viscoélastique obéissant à une loi de comportement semiempirique. Ils appliquent la méthode de raccordement des développements asymptotiques afin de déterminer le profil de vitesses à l'intérieur du jet, et l'entraînement du fluide extérieur. Les résultats obtenus illustrent l'influence de l'élasticité sur le champ de vitesse et la présence d'un gradient de pression à l'intérieur du jet. Les lignes de courant obtenues montrent que le fluide externe est aspiré vers l'axe du jet.

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Summary A two-dimensional laminar free jet of a viscoelastic fluid following a semiempiric constitutive equation is studied. The method of matching asymptotic expansions is applied to determine the velocity profiles inside the jet and the entrainment of the external fluid. The results thus obtained highlight the influence of elasticity on the velocity field and the presence of a pressure gradient inside the jet. The streamlines obtained show that the external fluid is sucked in towards the axis of the jet.

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Zusammenfassung Es wird der laminare zweidimensionale Freistrahl einer viskoelastischen Flüssigkeit, die einem halbempirischen Stoffgesetz folgt, untersucht. Asymptotische Entwicklungen werden aneinandergefügt, um die Geschwindigkeitsverteilung in der Strahlströmung und die Ansaugkraft der äußeren Flüssigkeit zu bestimmen. Die erzielten Ergebnisse zeigen den Einfluß der Elastizität auf die Geschwindigkeitsverteilung und das Bestehen eines Druckgradienten innerhalb der Strahlströmung. Die abgeleiteten Stromlinien zeigen weiter, daß die äußere Flüssigkeit zur Strahlachse hin angesaugt wird.

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A ₁;A ₂;A ₃ tenseurs de Rivlin-Ericksen - A constante définie par [27] - D domaine d'écoulement - f ₁();f ₀() fonctions définies par la transformation [20] - I tenseur unité - J nombre adimensionnel [12] - L longueur de référence - M flux total d'impulsion [19]m: µ/ - N _Re nombre de Reynolds - N _w nombre de Weissenberg - n indice de comportement - p pression - s indice de comportement «élastique» - T tenseur des contraintes - U ₀ vitesse de référence - u, v composantes du vecteur vitesse - x, y coordonnées cartésiennes - Y coordonnée de «couche limite» [9] - Z variable complexe - angle entre les parois de la fente - paramètre de perturbation - variable affine [20] - () fonction définie par [2c] - coefficient d'élasticité - fonction de viscosité [2a] - µ indice de consistance - masse volumique - ; fonctions de courant - fonction définie par [2b] - 2ème invariant principal du tenseurA ₁ Avec 7 figures     

Direct modeling of flow of FENE fluids

Direct simulations of macromolecular fluids are carried out for flows between parallel plates and in expanding and contracting channels. The macromolecules are modeled as FENE dumbbells with soft disks or Lennard-Jones dumbbell-dumbbell interactions. The results are presented in terms of profiles and contour plots of velocity, pressure, temperature, density, and flow fields. In addition the data for potential energy, shear stress, and the normal components of the stress tensor are collected. In general, an excellent agreement is found between the simulated profiles and the well-known flow structures, such as flow separation and formation of viscous eddies, indicating that micro-hydrodynamics is a viable tool in linking macroscopic phenomena with the underlying physical mechanisms. The simulations are performed in the Newtonian regime, for medium-size systems comprising up to 3888 dumbbells. This number is sufficiently large to control boundary and particle number effects. The flow is induced by gravity. The traditional stochastic (thermal) and periodic boundary conditions are employed. Also, diffusive boundary conditions, which could include a stagnant fluid layer and repulsive potential walls, are developed. The scaling problems, which are related to the application of a large external force in a microscopic system (of the size of the order 100 Å), result in extreme pressure and temperature gradients. In addition, the viscosity and thermal conductivity coefficients obtained from velocity and temperature profiles of the channel flow are presented. These results are confirmed independently from modeling of Couette flow by the SLLOD equations of motion and from the Evans algorithm for thermal conductivity.     

PVT of amorphous and crystalline polymers and their nanocomposites

The Pressure-Volume-Temperature (PVT) of polystyrene (PS), polyamide-6 (PA-6) and their clay-containing polymeric nanocomposites (CPNC) were determined at T = 300-600 K and P = 0.1-190 MPa, thus in the molten, glassy and semicrystalline phase. The melt and glass behavior was interpreted following the Simha-Somcynsky (S-S) cell-hole free volume theory while that of the semicrystalline phase using S-S and the Midha-Nanda-Simha-Jain (MNSJ) cell theory describing crystalline quantum interactions. The theoretical analysis yielded two sets of the interaction parameters, one from the S-S and the other from the MNSJ model. The derivative properties: the compressibility, κ, and thermal expansion coefficient, α, were computed as functions of T, P and clay content, w. These functions, crossing several transition regions, were significantly different for the amorphous PS than for the semicrystalline PA-6. The isobaric PS plots of κ and α vs. T detected secondary transitions at T_β/T_g ≈ 0.9 ± 0.1 and at T_c/T_g = 1.2 ± 0.1. Addition of clay severely affected the vitreous phase (physical aging). In PA-6 systems the behavior was distinctly different than in PS, viz. κ = κ(T) followed a similar function across the melting zone, while α = α(T) dependencies were dramatically different for the solid and molten phase. The theoretical functions in reduced variables provided good basis for explanation of the observed dependencies.     

Rhodium(I)‐Catalyzed Enantioselective Activation of Cyclobutanols: Formation of Cyclohexane Derivatives with Quaternary Stereogenic Centers

The activation of carbon–carbon σ bonds is a complementary method to access uncommon and difficult‐to‐prepare organometallic species. Herein, we describe the activation of tert‐cyclobutanols through an enantioselective insertion of a chiral rhodium(I) complex into the C? C σ bond of the cyclobutane, forming a quaternary stereogenic center and an alkyl‐rhodium functionality that initiates ring‐closure reactions. This technology provides access to a variety of substituted cyclohexane derivatives with quaternary stereogenic centers. The formation of different product families can be controlled by the employed set of reaction conditions and additives. In general, high yields and excellent enantioselectivities of up to 99 % ee are obtained.