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Kinds of Phys Terms modified by Phys Selected AbstractsHydrogen Balmer Spectrum from a High-Pressure Arc Discharge: RevisitedCONTRIBUTIONS TO PLASMA PHYSICS, Issue 4-5 2007B. Omar Abstract The interpretation of hydrogen Balmer spectra emitted from a high-pressure arc discharge (Radtke and Günther, Contrib. Plasma Phys. 26, 143 (1986)) is re-examined. Assuming local thermodynamic equilibrium, synthetic Balmer spectra are calculated for given temperature and density conditions. Radiation transport is accounted for using a one-dimensional plasma layer model. The lineshape of bound-bound transitions is determined using a microscopic quantum-statistical approach. Free-free and free-bound contributions are added by taking expressions from literature. Comparing the synthetic spectra with experimental ones, plasma temperature and density conditions are inferred. The plasma parameters are confronted with theoretical results for the compositions of dense plasma. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Optimal separation times for electrical field flow fractionation with Couette flowsELECTROPHORESIS, Issue 20 2008Jennifer Pascal Abstract The prediction of optimal times of separation as a function of the applied electrical field and cation valence have been studied for the case of field flow fractionation [Martin M., Giddings J. C., J. Phys. Chem. 1981, 85, 727] with charged solutes. These predictions can be very useful to a priori design or identify optimal operating conditions for a Couette-based device for field flow fractionation when the orthogonal field is an electrical field. Mathematically friendly relationships are obtained by applying the method of spatial averaging to the solute species continuity equation; this is accomplished after the role of the capillary geometrical dimensions on the applied electrical field equations has been assessed [Oyanader M. A., Arce P., Electrophoresis 2005; 26, 2857]. Moreover, explicit analytical expressions are derived for the effective parameters, i.e. diffusivity and convective velocity as functions of the applied (orthogonal) electrical field. These effective transport parameters are used to study the effect of the cation valence of the solutes and of the magnitude of the applied orthogonal electrical field on the values of the optimal time of separation. These parameters play a significant role in controlling the optimal separation time, leading to a family of minimum values, for particular magnitudes of the applied orthogonal electrical field. [source] Comprehensive Modeling of Ion Conduction of Nanosized CaF2/BaF2 Multilayer HeterostructuresADVANCED FUNCTIONAL MATERIALS, Issue 1 2009Xiangxin Guo Abstract Molecular beam epitaxy-grown CaF2/BaF2 heterolayers are a demonstration of the potential of nanoionics. It has been shown that ion conductivities both parallel and perpendicular to the interfaces increase with decrease in interfacial spacing. This size effect was attributed to the thermodynamically necessary redistribution of the mobile fluoride ions (N. Sata, K. Eberl, K. Eberman, J. Maier, Nature 2000, 408, 946; X. X. Guo, I. Matei, J.-S. Lee, J. Maier, Appl. Phys. Lett. 2007, 91, 103102). On this basis, the striking phenomenon of an upward bending in the effective parallel conductivity as a function of inverse interfacial spacing for low temperatures (T,,,593,K) has been satisfactorily explained by application of a modified Mott,Schottky model for BaF2 (X.X. Guo, I. Matei, J. Jamnik, J.-S. Lee, J. Maier, Phys. Rev. B 2007, 76, 125429). This model was further confirmed by measurements perpendicular to the interfaces that offer complementary information on the more resistive parts. Here a successful comprehensive modeling of parallel and perpendicular conductivities for the whole parameter range, namely for interfacial spacings ranging from 6 to 200,nm and investigated temperatures ranging from 455 to 833,K, is presented. The model is based on literature data for carrier mobilities and Frenkel reaction constants and the assumption of a pronounced F, redistribution. Given the fact that an impurity content that was experimentally supported is taken into account and apart from minor assumptions concerning profile homogeneity, the only fit parameter is the space charge potential. In particular, it is worth mentioning that in BaF2 the low temperature Mott,Schottky space charge zone which is determined by impurities changes over, at high temperatures, into a Gouy,Chapman situation owing to increased thermal disorder. (The situation in CaF2 is of Gouy,Chapman type at all temperatures.) [source] Homogenization-based analysis of anisotropic damage in brittle materials with unilateral effect and interactions between microcracksINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2009Q. Z. Zhu Abstract This paper is devoted to micromechanical modeling of induced anisotropic damage in brittle geomaterials. The formulation of the model is based on a proper homogenization procedure by taking into account unilateral effects and interactions between microcracks. The homogenization procedure is developed in the framework of Eshelby's inclusion solution and Ponte-Castaneda and Willis (J. Mech. Phys. Solids 1995; 43:1919,1951) estimate. The homogenization technique is combined with the thermodynamics framework at microscopic level for the determination of damage evolution law. A rigorous crack opening,closure transition condition is established and an energy-release-rate-based damage criterion is proposed. Computational aspects on the implementation of micromechanical model are also discussed. The proposed model is evaluated by comparing numerical predictions with experimental data for various laboratory tests on concrete. Parametric studies on unilateral effects and influences of microcracks interactions are finally performed and analyzed. Copyright © 2008 John Wiley & Sons, Ltd. [source] A multiscale modeling of damage and time-dependent behavior of cohesive rocksINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 5 2009A. Abou-Chakra Guéry Abstract The present paper deals with a micromechanical approach to modeling the time-dependent mechanical behavior of a class of cohesive geomaterials. The considered material is Callovo-Oxfordian argillite, which is mainly composed of three constituents: an elastoviscoplastic clay matrix, elastic quartz minerals, and elastic damaged calcite grains. The macroscopic constitutive law is obtained by adapting the incremental method proposed by Hill (J. Mech. Phys. Solids 1965; 13:89,101). Its unified formulation allows a description of not only the time-dependent behavior of the argillite but also its elastoplastic damage response. The developed model is first validated by comparison with finite element solutions and then it is applied to the prediction of argillites' macroscopic responses in connection with their mineralogical compositions. The validity of the model is checked through comparisons between the model's predictions and experimental data. Copyright © 2008 John Wiley & Sons, Ltd. [source] The Reissner,Sagoci problem for a transversely isotropic half-spaceINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2006Mohammad Rahimian Abstract A transversely isotropic linear elastic half-space, z,0, with the isotropy axis parallel to the z -axis is considered. The purpose of the paper is to determine displacements and stresses fields in the interior of the half-space when a rigid circular disk of radius a completely bonded to the surface of the half-space is rotated through a constant angle ,0. The region of the surface lying out with the circle r,a, is free from stresses. This problem is a type of Reissner,Sagoci mixed boundary value problems. Using cylindrical co-ordinate system and applying Hankel integral transform in the radial direction, the problem may be changed to a system of dual integral equations. The solution of the dual integral equations is obtained by an approach analogous to Sneddon's (J. Appl. Phys. 1947; 18:130,132), so that the circumferential displacement and stress fields inside the medium are obtained analytically. The same problem has already been approached by Hanson and Puja (J. Appl. Mech. 1997; 64:692,694) by the use of integrating the point force potential functions. It is analytically proved that the present solution, although of a quite different form, is equivalent to that given by Hanson and Puja. To illustrate the solution, a few plots are provided. The displacements and the stresses in a soil deposit due to a rotationally symmetric force or boundary displacement may be obtained using the results of this paper. Copyright © 2006 John Wiley & Sons, Ltd. [source] Modelling poroelastic hollow cylinder experiments with realistic boundary conditionsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2004S. Jourine Abstract A general poroelastic solution for axisymmetrical plane strain problems with time dependent boundary conditions is developed in Laplace domain. Time-domain results are obtained using numerical inversion of the Laplace transform. Previously published solutions can be considered as special cases of the proposed solution. In particular, we could reproduce numerical results for solid and hollow poroelastic cylinders with suddenly applied load/pressure (Rice and Cleary, Rev. Geophys. Space Phys. 1976; 14:227; Schmitt, Tait and Spann, Int. J. Rock Mech. Min. Sci. 1993; 30:1057; Cui and Abousleiman, ASCE J. Eng. Mech. 2001; 127:391). The new solution is used to model laboratory tests on thick-walled hollow cylinders of Berea sandstone subjected to intensive pressure drawdown. In the experiments, pressure at the inner boundary of the hollow cylinder is observed to decline exponentially with a decay constant of 3,5 1/s. It is found that solutions with idealized step-function type inner boundary conditions overestimate the induced tensile radial stresses considerably. Although basic poroelastic phenomena can be modelled properly at long time following a stepwise change in pressure, realistic time varying boundary conditions predict actual rock behaviour better at early time. Experimentally observed axial stresses can be matched but appear to require different values for , and , than are measured at long time. The proposed solution can be used to calculate the stress and pore pressure distributions around boreholes under infinite/finite boundary conditions. Prospective applications include investigating the effect of gradually changing pore pressure, modelling open-hole cavity completions, and describing the phenomenon of wellbore collapse (bridging) during oil or gas blowouts. Copyright © 2004 John Wiley & Sons, Ltd. [source] Transient deformation of a poroelastic channel bedINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 13 2002P.C. Hsieh Abstract The coupled transient response of a poroelastic bed form due to stream flow and non-linear water waves is investigated numerically. The theory of potential flow is applied to channel flow while Biot's theory of poroelasticity (J. Appl. Phys. 1962; 33(4):1482) is adopted to deal with the deformable porous bed. A boundary-fitted co-ordinate system is used to calculate the variation in the bed form. The result of a simple periodic wave form over a soft poroelastic bed agrees well with the analytical solution of Hsieh et al. (J. Eng. Mech., ASCE 2000; 126(10):1064). However, due to the rapidly damping second dilatational wave inside the soft poroelastic bed, the solution for transient bed form near the interface is not easy to compute accurately. In order to overcome this difficulty, a simplified numerical model based on the boundary layer correction concept proposed by Hsieh et al. (2000) is established, which neglects Darcy's terms. The transient deformation of an irregular poroelastic bed that includes a trench and a downward step at the channel bed is simulated successfully. Copyright © 2002 John Wiley & Sons, Ltd. [source] Deformations caused by the movements of shear and tensile faultsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2001Guang Y. Sheu Abstract Earlier solutions of deformations resulting from the movements of shear and tensile faults in a half space (Bull. Seismol. Soc. Amer. 1985; 75:1135, 1992; 82:1018) have been revised in view of cross-anisotropic stress,strain relationships. The dislocation theory (Canad. J. Phys. 1958; 36:192) is reviewed and the displacement field due to a concentrated force in an anisotropic half space is solved analytically for developing the current research. A fault is simulated as a point source of strain nuclei in applying the dislocation theory. Data (Terr. Atmos. Oceanic Sci. 2000; 11(3):591, 631) that were used to study the Chi-Chi earthquake (ML=7.3; 1999/9/21 AM 1:47) are introduced to compare the solution with the isotropic results. Results indicate that the anisotropy of stress,strain relationships does affect the results of predicted deformations. Copyright © 2001 John Wiley & Sons, Ltd. [source] A combination of implicit and adaptative upwind tools for the numerical solution of incompressible free surface flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2007V. G. Ferreira Abstract This paper is concerned with the numerical solutions of time dependent two-dimensional incompressible flows. By using the primitive variables of velocity and pressure, the Navier,Stokes and mass conservation equations are solved by a semi-implicit finite difference projection method. A new bounded higher order upwind convection scheme is employed to deal with the non-linear (advective) terms. The procedure is an adaptation of the GENSMAC (J. Comput. Phys. 1994; 110:171,186) methodology for calculating confined and free surface fluid flows at both low and high Reynolds numbers. The calculations were performed by using the 2D version of the Freeflow simulation system (J. Comp. Visual. Science 2000; 2:199,210). In order to demonstrate the capabilities of the numerical method, various test cases are presented. These are the fully developed flow in a channel, the flow over a backward facing step, the die-swell problem, the broken dam flow, and an impinging jet onto a flat plate. The numerical results compare favourably with the experimental data and the analytical solutions. Copyright © 2006 John Wiley & Sons, Ltd. [source] Explicit coupled thermo-mechanical finite element model of steel solidificationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2009Seid Koric Abstract The explicit finite element method is applied in this work to simulate the coupled and highly non-linear thermo-mechanical phenomena that occur during steel solidification in continuous casting processes. Variable mass scaling is used to efficiently model these processes in their natural time scale using a Lagrangian formulation. An efficient and robust local,global viscoplastic integration scheme (Int. J. Numer. Meth. Engng 2006; 66:1955,1989) to solve the highly temperature- and rate-dependent elastic,viscoplastic constitutive equations of solidifying steel has been implemented into the commercial software ABAQUS/Explicit (ABAQUS User Manuals v6.7. Simulia Inc., 2007) using a VUMAT subroutine. The model is first verified with a known semi-analytical solution from Weiner and Boley (J. Mech. Phys. Solids 1963; 11:145,154). It is then applied to simulate temperature and stress development in solidifying shell sections in continuous casting molds using realistic temperature-dependent properties and including the effects of ferrostatic pressure, narrow face taper, and mechanical contact. Example simulations include a fully coupled thermo-mechanical analysis of a billet-casting and thin-slab casting in a funnel mold. Explicit temperature and stress results are compared with the results of an implicit formulation and computing times are benchmarked for different problem sizes and different numbers of processor cores. The explicit formulation exhibits significant advantages for this class of contact-solidification problems, especially with large domains on the latest parallel computing platforms. Copyright © 2008 John Wiley & Sons, Ltd. [source] An accelerated FFT algorithm for thermoelastic and non-linear compositesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2008V. Vinogradov Abstract A fast numerical algorithm to compute the local and overall responses of non-linear composite materials is developed. This alternative formulation allows us to improve the convergence of the existing method of Moulinec and Suquet (e.g. Comput. Meth. Appl. Mech. Eng. 1998; 157(1,2):69,94). In the present method, a non-linear elastic (or conducting) material is replaced by infinitely many locally linear thermoelastic materials with moduli that depend on the values of the local fields. This makes it possible to use the advantages of an algorithm developed by Eyre and Milton (Eur. Phys. J. Appl. Phys. 1999; 6(1):41,47), which has faster convergence. The method is applied to compute the local fields as well as the effective response of non-linear conducting and elastic periodic composites. Copyright © 2008 John Wiley & Sons, Ltd. [source] Theory and finite element computation of cyclic martensitic phase transformation at finite strainINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2008Erwin Stein Abstract A generalized variational formulation, including quasi-convexification of energy wells for arbitrarily many martensitic variants in case of mono-crystals for linearized strains, was developed by Govindjee and Miehe (Comp. Meth. Appl. Mech. Eng. 2001; 191(3,5):215,238) and computationally extended by Stein and Zwickert (Comput. Mech. 2006; in press). This work is generalized here for finite strain kinematics with monotonous hyperelastic stress,strain functions in order to account for large transformation strains that can reach up to 15%. A major theoretical and numerical difficulty herein is the convexification of the finite deformation phase transformation (PT) problems for multiple phase variants, n,2. A lower bound of the mixing energy is provided by the Reuss bound in case of linear kinematics and an arbitrary number of variants, shown by Govindjee et al. (J. Mech. Phys. Solids 2003; 51(4):I,XXVI). In case of finite strains, a generalized representation of free energy of mixing is introduced for a quasi-Reuss bound, which in general holds for n,2. Numerical validation of the used micro,macro material model is presented by comparing verified numerical results with the experimental data for Cu82Al14Ni4 monocrystals for quasiplastic PT, provided by Xiangyang et al. (J. Mech. Phys. Solids 2000; 48:2163,2182). The zigzag-type experimental stress,strain curve within PT at loading, called ,yield tooth', is approximated within the finite element analysis by a smoothly decreasing and then increasing axial stress which could not be achieved with linearized kinematics yielding a constant axial stress during PT. Copyright © 2007 John Wiley & Sons, Ltd. [source] A hybrid Padé ADI scheme of higher-order for convection,diffusion problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2010Samir KaraaArticle first published online: 8 SEP 200 Abstract A high-order Padé alternating direction implicit (ADI) scheme is proposed for solving unsteady convection,diffusion problems. The scheme employs standard high-order Padé approximations for spatial first and second derivatives in the convection-diffusion equation. Linear multistep (LM) methods combined with the approximate factorization introduced by Beam and Warming (J. Comput. Phys. 1976; 22: 87,110) are applied for the time integration. The approximate factorization imposes a second-order temporal accuracy limitation on the ADI scheme independent of the accuracy of the LM method chosen for the time integration. To achieve a higher-order temporal accuracy, we introduce a correction term that reduces the splitting error. The resulting scheme is carried out by repeatedly solving a series of pentadiagonal linear systems producing a computationally cost effective solver. The effects of the approximate factorization and the correction term on the stability of the scheme are examined. A modified wave number analysis is performed to examine the dispersive and dissipative properties of the scheme. In contrast to the HOC-based schemes in which the phase and amplitude characteristics of a solution are altered by the variation of cell Reynolds number, the present scheme retains the characteristics of the modified wave numbers for spatial derivatives regardless of the magnitude of cell Reynolds number. The superiority of the proposed scheme compared with other high-order ADI schemes for solving unsteady convection-diffusion problems is discussed. A comparison of different time discretizations based on LM methods is given. Copyright © 2009 John Wiley & Sons, Ltd. [source] Performance of very-high-order upwind schemes for DNS of compressible wall-turbulenceINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2010G. A. Gerolymos Abstract The purpose of the present paper is to evaluate very-high-order upwind schemes for the direct numerical simulation (DNS) of compressible wall-turbulence. We study upwind-biased (UW) and weighted essentially nonoscillatory (WENO) schemes of increasingly higher order-of-accuracy (J. Comp. Phys. 2000; 160:405,452), extended up to WENO17 (AIAA Paper 2009-1612, 2009). Analysis of the advection,diffusion equation, both as ,x,0 (consistency), and for fixed finite cell-Reynolds-number Re,x (grid-resolution), indicates that the very-high-order upwind schemes have satisfactory resolution in terms of points-per-wavelength (PPW). Computational results for compressible channel flow (Re,[180, 230]; M,CL,[0.35, 1.5]) are examined to assess the influence of the spatial order of accuracy and the computational grid-resolution on predicted turbulence statistics, by comparison with existing compressible and incompressible DNS databases. Despite the use of baseline O(,t2) time-integration and O(,x2) discretization of the viscous terms, comparative studies of various orders-of-accuracy for the convective terms demonstrate that very-high-order upwind schemes can reproduce all the DNS details obtained by pseudospectral schemes, on computational grids of only slightly higher density. Copyright © 2009 John Wiley & Sons, Ltd. [source] Numerical implementation of Aristov,Pukhnachev's formulation for axisymmetric viscous incompressible flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2010N. P. Moshkin Abstract In the present work a finite-difference technique is developed for the implementation of a new method proposed by Aristov and Pukhnachev (Doklady Phys. 2004; 49(2):112,115) for modeling of the axisymmetric viscous incompressible fluid flows. A new function is introduced that is related to the pressure and a system similar to the vorticity/stream function formulation is derived for the cross-flow. This system is coupled to an equation for the azimuthal velocity component. The scheme and the algorithm treat the equations for the cross-flow as an inextricably coupled system, which allows one to satisfy two conditions for the stream function with no condition on the auxiliary function. The issue of singularity of the matrix is tackled by adding a small parameter in the boundary conditions. The scheme is thoroughly validated on grids with different resolutions. The new numerical tool is applied to the Taylor flow between concentric rotating cylinders when the upper and lower lids are allowed to rotate independently from the inner cylinder, while the outer cylinder is held at rest. The phenomenology of this flow is adequately represented by the numerical model, including the hysteresis that takes place near certain specific values of the Reynolds number. Thus, the present results can be construed to demonstrate the viability of the new model. The success can be attributed to the adequate physical nature of the auxiliary function. The proposed technique can be used in the future for in-depth investigations of the bifurcation phenomena in rotating flows. Copyright © 2009 John Wiley & Sons, Ltd. [source] A streamfunction,velocity approach for 2D transient incompressible viscous flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2010Jiten C. Kalita Abstract We recently proposed (J. Comput. Phys. 2005; 207(1):52,68) a new paradigm for solving the steady-state two-dimensional (2D) Navier,Stokes (N,S) equations using a streamfunction,velocity (,,v) formulation. This formulation was shown to avoid the difficulties associated with the traditional formulations (primitive variables and streamfunction-vorticity formulations). The new formulation was found to be second-order accurate and was found to yield accurate solutions of a number of fluid flow problems. In this paper, we extend the ideas and propose a second-order implicit, unconditionally stable ,,v formulation for the unsteady incompressible N,S equations. The method is used to solve several 2D time-dependent fluid flow problems, including the flow decayed by viscosity problem with analytical solution, the lid-driven square cavity problem, the backward-facing step problem and the flow past a square prism problem. For the problems with known exact solutions, our coarse grid transient solutions are extremely close to the analytical ones even for high Reynolds numbers (Re). For the driven cavity problem, our time-marching steady-state solutions up to Re=7500 provide excellent matches with established numerical results, and for Re=10000, our study concludes that the asymptotic stable solution is periodic as has been found by other authors in recent studies. For the backward step problem, our numerical results are in excellent agreement with established numerical and experimental results. Finally, for the flow past a square prism, we have very successfully simulated the von Kármán vortex street for Re=200. Copyright © 2009 John Wiley & Sons, Ltd. [source] A level set-based immersed interface method for solving incompressible viscous flows with the prescribed velocity at the boundaryINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2010Zhijun Tan Abstract A second-order accurate immersed interface method (IIM) is presented for solving the incompressible Navier,Stokes equations with the prescribed velocity at the boundary, which is an extension of the IIM of Le et al. (J. Comput. Phys. 2006; 220:109,138) to a level set representation of the boundary in place of the Lagrangian representation of the boundary using control points on a uniform Cartesian grid. In order to enforce the prescribed velocity boundary condition, the singular forces at the immersed boundary are applied on the fluid. These forces are related to the jump in pressure and the jumps in the derivatives of both the pressure and velocity, and are approximated via using the local Hermite cubic spline interpolation. The strength of singular forces is determined by solving a small system of equations at each time step. The Navier,Stokes equations are discretized via using finite difference method with the incorporation of jump conditions on a staggered Cartesian grid and solved by a second-order accurate projection method. Numerical results demonstrate the accuracy and ability of the proposed method to simulate the viscous flows in irregular domains. Copyright © 2009 John Wiley & Sons, Ltd. [source] Fifth-order Hermitian schemes for computational linear aeroacousticsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2007Article first published online: 17 APR 200, G. Capdeville Abstract We develop a class of fifth-order methods to solve linear acoustics and/or aeroacoustics. Based on local Hermite polynomials, we investigate three competing strategies for solving hyperbolic linear problems with a fifth-order accuracy. A one-dimensional (1D) analysis in the Fourier series makes it possible to classify these possibilities. Then, numerical computations based on the 1D scalar advection equation support two possibilities in order to update the discrete variable and its first and second derivatives: the first one uses a procedure similar to that of Cauchy,Kovaleskaya (the ,,-P5 scheme'); the second one relies on a semi-discrete form and evolves in time the discrete unknowns by using a five-stage Runge,Kutta method (the ,RGK-P5 scheme'). Although the RGK-P5 scheme shares the same local spatial interpolator with the ,-P5 scheme, it is algebraically simpler. However, it is shown numerically that its loss of compactness reduces its domain of stability. Both schemes are then extended to bi-dimensional acoustics and aeroacoustics. Following the methodology validated in (J. Comput. Phys. 2005; 210:133,170; J. Comput. Phys. 2006; 217:530,562), we build an algorithm in three stages in order to optimize the procedure of discretization. In the ,reconstruction stage', we define a fifth-order local spatial interpolator based on an upwind stencil. In the ,decomposition stage', we decompose the time derivatives into simple wave contributions. In the ,evolution stage', we use these fluctuations to update either by a Cauchy,Kovaleskaya procedure or by a five-stage Runge,Kutta algorithm, the discrete variable and its derivatives. In this way, depending on the configuration of the ,evolution stage', two fifth-order upwind Hermitian schemes are constructed. The effectiveness and the exactitude of both schemes are checked by their applications to several 2D problems in acoustics and aeroacoustics. In this aim, we compare the computational cost and the computation memory requirement for each solution. The RGK-P5 appears as the best compromise between simplicity and accuracy, while the ,-P5 scheme is more accurate and less CPU time consuming, despite a greater algebraic complexity. Copyright © 2007 John Wiley & Sons, Ltd. [source] Multiple semi-coarsened multigrid method with application to large eddy simulationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2006F. E. Ham Abstract The Multiple Semi-coarsened Grid (MSG) multigrid method of Mulder (J. Comput. Phys. 1989; 83:303,323) is developed as a solver for fully implicit discretizations of the time-dependent incompressible Navier,Stokes equations. The method is combined with the Symmetric Coupled Gauss,Seidel (SCGS) smoother of Vanka (Comput. Methods Appl. Mech. Eng. 1986; 55:321,338) and its robustness demonstrated by performing a number of large-eddy simulations, including bypass transition on a flat plate and the turbulent thermally-driven cavity flow. The method is consistently able to reduce the non-linear residual by 5 orders of magnitude in 40,80 work units for problems with significant and varying coefficient anisotropy. Some discussion of the parallel implementation of the method is also included. Copyright © 2005 John Wiley & Sons, Ltd. [source] A least square extrapolation method for the a posteriori error estimate of the incompressible Navier Stokes problemINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2005M. Garbey Abstract A posteriori error estimators are fundamental tools for providing confidence in the numerical computation of PDEs. To date, the main theories of a posteriori estimators have been developed largely in the finite element framework, for either linear elliptic operators or non-linear PDEs in the absence of disparate length scales. On the other hand, there is a strong interest in using grid refinement combined with Richardson extrapolation to produce CFD solutions with improved accuracy and, therefore, a posteriori error estimates. But in practice, the effective order of a numerical method often depends on space location and is not uniform, rendering the Richardson extrapolation method unreliable. We have recently introduced (Garbey, 13th International Conference on Domain Decomposition, Barcelona, 2002; 379,386; Garbey and Shyy, J. Comput. Phys. 2003; 186:1,23) a new method which estimates the order of convergence of a computation as the solution of a least square minimization problem on the residual. This method, called least square extrapolation, introduces a framework facilitating multi-level extrapolation, improves accuracy and provides a posteriori error estimate. This method can accommodate different grid arrangements. The goal of this paper is to investigate the power and limits of this method via incompressible Navier Stokes flow computations. Copyright © 2005 John Wiley & Sons, Ltd. [source] Numerical simulation of three-dimensional free surface flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2003V. Maronnier Abstract A numerical model is presented for the simulation of complex fluid flows with free surfaces in three space dimensions. The model described in Maronnier et al. (J. Comput. Phys. 1999; 155(2) : 439) is extended to three dimensional situations. The mathematical formulation of the model is similar to that of the volume of fluid (VOF) method, but the numerical procedures are different. A splitting method is used for the time discretization. At each time step, two advection problems,one for the predicted velocity field and the other for the volume fraction of liquid,are to be solved. Then, a generalized Stokes problem is solved and the velocity field is corrected. Two different grids are used for the space discretization. The two advection problems are solved on a fixed, structured grid made out of small cubic cells, using a forward characteristic method. The generalized Stokes problem is solved using continuous, piecewise linear stabilized finite elements on a fixed, unstructured mesh of tetrahedrons. The three-dimensional implementation is discussed. Efficient postprocessing algorithms enhance the quality of the numerical solution. A hierarchical data structure reduces memory requirements. Numerical results are presented for complex geometries arising in mold filling. Copyright © 2003 John Wiley & Sons, Ltd. [source] An approximate projection method for incompressible flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2002David E. Stevens This paper presents an approximate projection method for incompressible flows. This method is derived from Galerkin orthogonality conditions using equal-order piecewise linear elements for both velocity and pressure, hereafter Q1Q1. By combining an approximate projection for the velocities with a variational discretization of the continuum pressure Poisson equation, one eliminates the need to filter either the velocity or pressure fields as is often needed with equal-order element formulations. This variational approach extends to multiple types of elements; examples and results for triangular and quadrilateral elements are provided. This method is related to the method of Almgren et al. (SIAM J. Sci. Comput. 2000; 22: 1139,1159) and the PISO method of Issa (J. Comput. Phys. 1985; 62: 40,65). These methods use a combination of two elliptic solves, one to reduce the divergence of the velocities and another to approximate the pressure Poisson equation. Both Q1Q1 and the method of Almgren et al. solve the second Poisson equation with a weak error tolerance to achieve more computational efficiency. A Fourier analysis of Q1Q1 shows that a consistent mass matrix has a positive effect on both accuracy and mass conservation. A numerical comparison with the widely used Q1Q0 (piecewise linear velocities, piecewise constant pressures) on a periodic test case with an analytic solution verifies this analysis. Q1Q1 is shown to have comparable accuracy as Q1Q0 and good agreement with experiment for flow over an isolated cubic obstacle and dispersion of a point source in its wake. Copyright © 2002 John Wiley & Sons, Ltd. [source] Shock tube study of 1,3,5-triazine dissociation and relaxation and relaxation of pyrazineINTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 4 2010Hui Xu The three-body dissociation of 1,3,5-triazine (s-triazine, s-C3H3N3 , 3HCN) has been observed in incident shock waves with the laser-schlieren technique. The experiments use 5% triazine/Kr and cover 1630,2350 K for 100,600 Torr. These experiments show dissociation rates with strong falloff and a slight but fully expected pressure dependence. The dissociation is without secondary reaction save for a possible, but rather unlikely, contribution from the isomerization HCN , HNC. Electronic structure calculations of the transition-state properties (G3B3, HL1, Eo = 84.6 kcal/mol) are used to construct a Rice,Ramsperger,Kassel,Marcus (RRKM) model whose fit to the rate measurements suggests a ,,E,down of 1200 cm,1. However, a seemingly better fit is achieved using the barrier of 81 kcal/mol proposed by Dyakov et al. (J. Phys. Chem. A 2007, 111, 9591,9599). With this barrier k, (s,1) = 5.3 × 1016 exp(,86.6(kcal/mol)/RT), and the fit now accepts the more routine ,,E,down = 126(T/298)0.9. It seems the dissociation most likely occurs by a direct, one-step, "triple" dissociation to 3HCN, although the present experiments cannot rule out a multistep process. Vibrational relaxation of the triazine was also examined in 5% and 20% mixtures with Kr over 770,1500 K for pressures between 6 and 14 Torr. Relaxation is very fast, with a slight inverse temperature dependence, P, rising from 100 to 200 ns-atm over the full temperature range. Integrated gradients are in good accord with calculated total changes in density, indicating a single exponential relaxation. A separate investigation of relaxation in the related molecule pyrazine (500,1300 K, in 1% and 5% in Kr, between 13 and 66 Torr) is included. Again relaxation is rapid, but here the temperature dependence seems more normal, the relaxation times decreasing slightly with temperature. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 42: 211,220, 2010 [source] Rate constants for H + CH4, CH3 + H2, and CH4 dissociation at high temperatureINTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 11 2001J. W. Sutherland The Laser Photolysis-Shock Tube technique coupled with H-atom atomic resonance absorption spectrometry has been used to study the reaction, H + CH4 , CH3 + H2, over the temperature range, 928,1697 K. Shock-tube studies on the reverse of this reaction, CH3 + H2 , H + CH4, using CH3I dissociation in the presence of H2 yielded H-atom formation rates and rate constants for the reverse process over the temperature range, 1269,1806 K. These results were transformed (using well-established equilibrium constants) to the forward direction. The combined results for H + CH4 can be represented by an experimental three parameter expression, k = 6.78 × 10,21 T3.156 exp(,4406 K/T) cm3 molecule,1 s,1 (348,1950 K) that was evaluated from the present work and seven previous studies. Using this evaluation, disagreements between previously reported values for the dissociation of CH4 could be reconciled. The thermal decomposition of CH4 was then studied in Kr bath gas. The dissociation results agreed with the earlier studies and were theoretically modeled with the Troe formalism. The energy transfer parameter necessary to explain both the present results and those of Kiefer and Kumaran (J Phys Chem 1993, 97, 414) is, ,,,E,all/cm,1 = 0.3323 T0.7. The low temperature data on the reverse reaction, H + CH3 (in He) from Brouard et al. (J Phys Chem 1989, 93, 4047) were also modeled with the Troe formalism. Lastly, the rate constant for H + CH4 was theoretically calculated using conventional transition state theory with Eckart tunneling corrections. The potential energy surface used was from Kraka et al. (J Chem Phys 1993, 99, 5306) and the derived T-dependence with this method agreed almost perfectly with the experimental evaluation. © 2001 John Wiley & Sons, Inc. Int J Chem Kinet 33: 669,684, 2001 [source] Nonrelativistic CI calculations for B+, B, and B, ground statesINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 15 2010César X. Almora-Díaz Abstract State of the art configuration interaction (CI) techniques are used to obtain the best possible nonrelativistic CI results for B+, B, and B, ground states using energy-optimized basis sets of 252, 294, and 294 radial Slater-type functions, respectively. For positive boron, E(B+) = ,24.348861 + ,Ebie = ,24.348883(1) a.u.(B) with a basis set incompleteness error ,Ebie = ,0.000022(1), in good agreement with the latest exponentially correlated Gaussian (ECG) result of ,24.348883 a.u.(B) of Komasa et al. (Phys Rev A, 2002, 65, 042507). For neutral B, E(B) = ,24.653837 ,0.000024(2) = ,24.653861(2), which is the most accurate ab initio estimate and lies slightly below a recent (not fully optimized) ECG result of ,24.653840 a.u.(B) of Bubin et al (J Chem Phys, 2009, 131, 044128). For negative boron, E(B,) = ,24.664014 ,0.000024(2) to which an energy error of ,0.000001 must be added to give ,24.664039(2), which is the first fully correlated ab initio result. Comparison with experimental values of ionization energy and electron affinity must await the results of corresponding relativistic calculations, in progress. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [source] HTSC cuprate phase diagram using a modified Boson,Fermion,Gossamer model describing competing orders, a quantum critical point and possible resonance complexINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 15 2009Richard H. Squire Abstract There has been considerable effort expended toward understanding high temperature superconductors (HTSC), and more specifically the cuprate phase diagram as a function of doping level. Yet, the only agreement seems to be that HTSC is an example of a strongly correlated material where Coulomb repulsion plays a major role. This manuscript proposes a model based on a Feshbach resonance pairing mechanism and competing orders. An initial BCS-type superconductivity at high doping is suppressed in the two particle channel by a localized preformed pair (PP) (Nozieres and Schmitt-Rink, J Low Temp Phys, 1985, 59, 980) (circular density wave) creating a quantum critical point. As doping continues to diminish, the PP then participates in a Feshbach resonance complex that creates a new electron (hole) pair that delocalizes and constitutes HTSC and the characteristic dome (Squire and March, Int J Quantum Chem, 2007, 107, 3013; 2008, 108, 2819). The resonant nature of the new pair contributes to its short coherence length. The model we propose also suggests an explanation (and necessity) for an experimentally observed correlated lattice that could restrict energy dissipation to enable the resonant Cooper pair to move over several correlation lengths, or essentially free. The PP density wave is responsible for the pseudogap as it appears as a "localized superconductor" since its density of states and quasiparticle spectrum are similar to those of a superconductor (Peierls,Fröhlich theory), but with no phase coherence between the PP. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] Convergence radii of the polarization expansion of intermolecular potentialsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 15 2009William H. Adams Abstract A new method is presented to evaluate convergence radii of the polarization expansion of interaction energies for pairs of atoms or molecules. The method is based on an analysis of the variation of the perturbed state vector as a function of the coupling constant , and does not require a calculation of perturbation corrections to high order. The convergence radii at infinite interatomic/intermolecular distances R, as well as a remarkably accurate representation of the R dependence of the convergence radii are obtained from simple calculations involving only monomer wave functions. For the interaction of the lithium and hydrogen atoms, the obtained convergence radii agree well with those obtained previously from the large-order calculations of Patkowski et al. (Patkowski et al., J Chem Phys, 2002, 117, 5124), but are expected to be considerably more accurate. Rigorous upper bounds and reasonable approximations to the convergence radii at R = , are obtained for the pairs of lithium, beryllium, boron, neon, and sodium atoms, as well as for the dimer consisting of two LiH molecules. For all the systems studied, the convergence radii are significantly smaller than the unity and rapidly decrease with the increase of the nuclear charge. It is hoped that the results of this investigation will help to analyze and eventually to compute the convergence radii of the symmetry-adapted perturbation theories which utilize the same partitioning of the Hamiltonian as the polarization expansion. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] The correlation contracted Schrödinger equation: An accurate solution of the G -particle-hole hypervirialINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 14 2009D. R. Alcoba Abstract The equation obtained by mapping the matrix representation of the Schrödinger equation with the 2nd-order correlation transition matrix elements into the 2-body space is the so called correlation contracted Schrödinger equation (CCSE) (Alcoba, Phys Rev A 2002, 65, 032519). As shown by Alcoba (Phys Rev A 2002, 65, 032519) the solution of the CCSE coincides with that of the Schrödinger equation. Here the attention is focused in the vanishing hypervirial of the correlation operator (GHV), which can be identified with the anti-Hermitian part of the CCSE. A comparative analysis of the GHV and the anti-Hermitian part of the contracted Schrödinger equation (ACSE) indicates that the former is a stronger stationarity condition than the latter. By applying a Heisenberg-like unitary transformation to the G -particle-hole operator (Valdemoro et al., Phys Rev A 2000, 61, 032507), a good approximation of the expectation value of this operator as well as of the GHV is obtained. The method is illustrated for the case of the Beryllium isoelectronic series as well as for the Li2 and BeH2 molecules. The correlation energies obtained are within 98.80,100.09% of the full-configuration interaction ones. The convergence of these calculations was faster when using the GHV than with the ACSE. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] Unusual low-intensity regime in laser-induced molecular photodissociationINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 14 2009R. Lefebvre Abstract Previous investigations of laser-induced photodissociation of a diatomic molecule (Atabek et al., Phys Rev A 2006, 74, 063412 and Atabek and Lefebvre, Phys Rev A 2008, 78, 043419) have shown that some of the Floquet eigenstates have the property that at some critical intensities their width is vanishing. These intensities are wavelength dependent. We exploit further this property by showing that by a proper choice of the wavelength, the critical intensity for a Floquet state originating from a given field-free vibrational state can be made vanishingly small. In such a case, the rate increases with intensity in an abnormally slow way. The wavelengths, which are required to reach this regime, can be derived accurately from the semiclassical criterion to obtain a zero-width resonance. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] | |||||||||||||||||||||||||