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Numerical Computation (numerical + computation)
Selected AbstractsNumerical computation of three-dimensional incompressible Navier,Stokes equations in primitive variable form by DQ methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2003C. Shu Abstract In this paper, the global method of differential quadrature (DQ) is applied to solve three-dimensional Navier,Stokes equations in primitive variable form on a non-staggered grid. Two numerical approaches were proposed in this work, which are based on the pressure correction process with DQ discretization. The essence in these approaches is the requirement that the continuity equation must be satisfied on the boundary. Meanwhile, suitable boundary condition for pressure correction equation was recommended. Through a test problem of three-dimensional driven cavity flow, the performance of two approaches was comparatively studied in terms of the accuracy. The numerical results were obtained for Reynolds numbers of 100, 200, 400 and 1000. The present results were compared well with available data in the literature. In this work, the grid-dependence study was done, and the benchmark solutions for the velocity profiles along the vertical and horizontal centrelines were given. Copyright © 2003 John Wiley & Sons, Ltd. [source] Numerical computation of cross-coupled algebraic Riccati equations related to H2/H, control problem for singularly perturbed systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 8 2004Hiroaki Mukaidani Abstract In this paper, we present a numerical algorithm to the cross-coupled algebraic Riccati equations(CARE) related to H2/H, control problems for singularly perturbed systems (SPS) by means of Newton's method. The resulting algorithm can be widely used to solve Nash game problems and robust control problems because the CARE is solvable even if the quadratic term has an indefinite sign. We prove that the resulting iterative algorithm has the property of the quadratic convergence. Using the solution of the CARE, we construct the high-order approximate H2/H, controller. Copyright © 2004 John Wiley & Sons, Ltd. [source] Numerical computation of a singular-state subarc in an economic optimal control modelOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 4 2006H. J. Oberle Abstract In this paper, optimal control problems (OCP) are considered which are characterized by a nonsmooth-state differential equation. More precisely, it is assumed that the right-hand side of the state equation is piecewise smooth and that the junction points between smooth subarcs are determined as roots of a state-dependent switching function. For this kind of OCP necessary conditions are developed. Special attention is paid to the situation that the switching function vanishes identically along a nontrivial subarc. Such subarcs, which are called singular-state subarcs, are investigated with respect to the necessary conditions and to the junction conditions. In this paper, we assume that the switching function is of first order with respect to the control. The theory is applied to an economic optimal control model due to Pohmer (Mikroökonomische Theorie der personellen Einkommens- und Vermögensverteilung. Studies in Contemporary Economics, vol. 16. Springer: Berlin, 1985), which describes the personal income distribution of a typical consumer, who wants to maximize the total utility of his lifetime by controlling the consumption, the rate of the total time used for working, and the rate of working time used for education and extended professional training. The state variables are the human capital and the capital itself. The utility function contains different parts which represent the influence of consumption, time of recreation, and human capital. Into this problem a parameter enters which describes the interest rate of capital. It is obvious that this parameter in general will differ for positive and negative values of the capital. Thus, the resulting OCP in a natural way becomes a nonsmooth one. For this problem, the necessary conditions are derived and numerical solutions are presented which are obtained by an indirect optimal control method. It turns out that for a certain distance of the positive and negative interest rate, the optimal solution contains a singular-state subarc. Copyright © 2006 John Wiley & Sons, Ltd. [source] Numerical computation of distortions in magnetic fields and induced currents in physiological solutions produced by microscope objectivesBIOELECTROMAGNETICS, Issue 7 2001Indira Chatterjee Abstract Identifying distortions produced by commonly employed microscope objectives and their components in uniform DC and 60 Hz AC magnetic fields is important in imaging studies involving exposure of cells to spatially uniform or nonuniform magnetic fields. In this study, DC and 60 Hz AC magnetic flux densities were numerically computed in the presence of finite element models of various components of commonly utilized microscope objectives, as well as a model of a complete objective. Also computed were the distortions in the current density induced by an applied time-varying magnetic field in a physiological buffer contained within a Petri dish. We show that the magnetic flux density could be increased up to 65% in the presence of the nickel,chrome plating of an objective housing and that the presence of ferromagnetic components like a screw or spring could produce peaks that are 7% higher than the undistorted value of magnetic flux density. In addition, a slight tilt of 1% in the objective with respect to the magnetic field could cause a 93% deviation in magnetic flux density from the unperturbed value. These results correlate well with previously published experimental measurements that showed the presence of significant and sometimes asymmetric distortions in both DC and 60 Hz magnetic fields. Moreover, this study further reports that induced current density changed up to 37% compared to values in the absence of the objective. The existence of distortions in applied magnetic fields and induced currents could affect the interpretation of results of cell function studies if it is assumed that the cells are exposed to uniform magnetic flux densities in the presence of a microscope objective. Such assumptions of uniform magnetic flux density could also account for the lack of reproducibility in several studies that examined changes in intracellular calcium by imaging techniques. Bioelectromagnetics 22:463,469, 2001. © 2001 Wiley-Liss, Inc. [source] Impulsive Dirac-delta forces in the rocking motionEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 7 2004F. Prieto Abstract In this work the classical theory of one block rocking motion is revisited. A Dirac-delta type interaction as impact mechanism is found to be an alternative for the traditional model. Numerical computations with this new formulation have shown that the agreement with the classical theory is excellent for the case of slender blocks and small displacements. Good agreement with experimental data has also been found for the case of arbitrary angles and slenderness. The approach presented in this paper opens new lines for further theoretical developments and computational applications. Copyright © 2004 John Wiley & Sons, Ltd. [source] Standing contact fatigue with a cylindrical indenterFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 7 2005J. DAHLBERG ABSTRACT A hardened steel cylinder was repeatedly pressed against a flat case-hardened steel specimen that was equally wide as the cylinder was long. Some contact end effects were noted as a result of limited plastic deformation. A strain gauge on the contact surface, just outside the contact and oriented perpendicular to the cylinder detected a surface strain when the cylinder was loaded. The non-zero surface strain was the result of boundary effects of the finite specimen. Four different types of contact fatigue cracks developed in and below the specimen contact surface. The cracks were named lateral, median, contact end and edge cracks. Changes in the measured surface strain values could be used to determine when the lateral and edge cracks developed. The order in which all four crack types typically developed was determined from optical crack observation at test termination, strain measurements and stress computations. Numerical computations using finite-element (FE) analyses were used to verify the surface strain behaviour due to loading and cracking; to verify contact end effects; crack locations and crack orientation by aid of the Findley multi-axial fatigue criterion. [source] Elastic waves at a corrugated interface between two dissimilar fibre-reinforced elastic half-spacesINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2007Sanasam Sarat Singh Abstract The reflection and transmission phenomena of elastic waves incident at a corrugated interface between two dissimilar fibre-reinforced elastic half-spaces have been analysed. Using Rayleigh method of approximation, the expressions of the reflection and transmission coefficients are obtained in closed form for the plane interface as well as for the first order approximation of the periodic interface , = d cos px. All these reflection and transmission coefficients of regular and irregular waves are found to be the functions of angle of incidence and elastic parameters of the media. Moreover, the coefficients of irregularly reflected and transmitted waves are found to be proportional to the amplitude of the corrugated interface and are functions of the frequency of the incident wave. Numerical computations have been performed for a specific model to compute these coefficients and results obtained are shown graphically. The results of Singh and Singh (Sadhana 2004; 29:249,257) and Ben-Menahem and Singh (Seismic Waves and Sources. Springer: New York) have been derived from our analysis as particular cases. Copyright © 2006 John Wiley & Sons, Ltd. [source] Plane SH-waves at a corrugated interface between two dissimilar perfectly conducting self-reinforced elastic half-spacesINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2006S. K. Tomar Abstract In this paper, we have attempted a problem of reflection and refraction of plane harmonic SH-wave at a corrugated interface between two different perfectly conducting self-reinforced elastic half-spaces. Rayleigh's method is employed to find out the expressions of reflection and refraction coefficients for first- and second-order approximation of the corrugation. The expressions of these coefficients show that they depend on the properties of half-spaces, angle of incidence, frequency of the incident wave and are strongly influenced by the corrugation of the interface. Numerical computations are performed for a particular model having special type of interface and the variation of these coefficients are depicted graphically against the angles of incidence, frequency parameter, corrugation parameter at different values of reinforcement parameters. Results of some earlier works are reduced as a particular case of this formulation. Copyright © 2005 John Wiley & Sons, Ltd. [source] Effect of phase change material on passive thermal heating of a greenhouseINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 4 2006Nisha Kumari Abstract In this study, a periodic analysis of a greenhouse with combination of phase change material (PCM) and insulation as a north wall has been developed for thermal heating. The thermal model is based on Fourier analysis. Effect of distribution of PCM thickness on plant and room air temperature has been studied in detail. The plant and room air temperature have been evaluated with and without north wall. Numerical computations have been carried out for a typical winter day of New Delhi. On the basis of numerical results, it is inferred that (i) there is a significant effect of PCM north wall and heat capacity of plant temperature during off-sunshine hour due to storage effect and (ii) the rate of heat flux inside greenhouse from north wall is maximum for least thickness of PCM. Copyright © 2005 John Wiley & Sons, Ltd. [source] Computational analysis of an instantaneous chemical reaction in a T-microreactorAICHE JOURNAL, Issue 6 2010Dieter Bothe Abstract We extend and apply a method for the numerical computation of convective and diffusive mixing in liquid systems with very fast irreversible chemical reaction to the case of unequal diffusivities. This approach circumvents the solution of stiff differential equations and, hence, facilitates the direct numerical simulation of reactive flows with quasi-instantaneous reactions. The method is validated by means of a neutralization reaction which is studied in a T-shaped micromixer and compared with existing experimental LIF-data. Because of their large are-to-volume ratio, microreactors are well suited for fast chemical reactions which are seriously affected by the slow diffusive transport in aqueous media. Numerical computations for different reactor dimensions reveal the fact that, in a dimensionless setting, the obtained conversion is independent of the reactor size, if the flow conditions are the same. This corresponds to an increase of space-time-yield proportional to the square of the inverse scale factor. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] New iterative equations for an E -plane T-junction in a parallel-plate waveguide using Green's functionMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 6 2003Yong H. Cho Abstract Reflection and transmission behaviors of an E-plane T-junction in a parallel-plate waveguide are theoretically investigated. Green's function and the iterative procedure are used to obtain the iterative equations for the Hz field modal coefficients. Numerical computations illustrate the characteristics of reflection and transmission powers in terms of frequency. A dominant-mode solution is presented and compared with higher-mode solutions. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 37: 447,449, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10945 [source] Experimental and Numerical Simulation Study of Heat Transfer Due to Confined Impinging Circular JetCHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 10 2007L. Chang-geng Abstract An experimental and numerical simulation study of heat transfer due to a confined impinging circular jet is presented. In this research, a stainless steel foil heated disk was used as the heat transfer surface of a simulated chip, and the thermocouples were mounted symmetrically along the diameter of the foil to measure the temperature distribution on the surface. Driven by a small pump, a circular air jet (1.5,mm and 1,mm in diameter) impinged on the heat-transfer surface with middle and low Reynolds numbers. The parameters, such as Reynolds number and ratio of height-to-diameter, were changed to investigate the radial distribution of the Nusselt number and the characteristics of heat transfer in the stagnation region. Numerical computations were performed by using several different turbulence models. In wall bounded turbulent flows, near-wall modeling is crucial. Therefore, the turbulence models enhanced wall treatment, such as the RNG ,-, model, may be superior for modeling impingement flows. The numerical results showed reasonable agreement with the experimental data for local heat transfer coefficient distributions. The impinging jet may be an effective method to solve the cooling problem of high power density electronic packaging. [source] Using linked markers to infer the age of a mutationHUMAN MUTATION, Issue 2 2001Bruce Rannala Abstract Advances in sequencing and genotyping technologies over the last decade have enabled geneticists to easily characterize genetic variation at the nucleotide level. Hundreds of genes harboring mutations associated with genetic disease have now been identified by positional cloning. Using variation at closely linked genetic markers, it is possible to predict the times in the past at which particular mutations arose. Such studies suggest that many of the rare mutations underlying human genetic disorders are relatively young. Studies of variation at genetic markers linked to particular mutations can provide insights into human geographic history, and historical patterns of natural selection and disease, that are not available from other sources. We review two approaches for estimating allele age using variation at linked genetic markers. A phylogenetic approach aims to reconstruct the gene tree underlying a sample of chromosomes carrying a particular mutation, obtaining a "direct" estimate of allele age from the age of the root of this tree. A population genetic approach relies on models of demography, mutation, and/or recombination to estimate allele age without explicitly reconstructing the gene tree. Phylogenetic methods are best suited for studies of ancient mutations, while population genetic methods are better suited for studies of recent mutations. Methods that rely on recombination to infer the ages of alleles can be fine-tuned by choosing linked markers at optimal map distances to maximize the information available about allele age. A limitation of methods that rely on recombination is the frequent lack of a fine-scale linkage map. Maximum likelihood and Bayesian methods for estimating allele age that rely on intensive numerical computation are described, as well as "composite" likelihood and moment-based methods that lead to simple estimators. The former provide more accurate estimates (particularly for large samples of chromosomes) and should be employed if computationally practical. Hum Mutat 18:87,100, 2001. © 2001 Wiley-Liss, Inc. [source] Dynamic response of soft poroelastic bed to linear water waves,a boundary layer correction approachINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2001Ping-Cheng Hsieh Abstract According to Chen et al. (Journal of Engineering Mechanics, ASCE 1997; 123(10):1041,1049.) a boundary layer exists within the porous bed and near the homogeneous-water/porous-bed interface when oscillatory water waves propagate over a soft poroelastic bed. This boundary layer makes the evaluation of the second kind of longitudinal wave inside the soft poroelastic bed very inaccurate. In this study, the boundary layer correction approach for the poroelastic bed is applied to the boundary value problem of linear oscillatory water waves propagating over a soft poroelastic bed. After the analyses of length scale and order of magnitude of physical variables are done, a perturbation expansion for the boundary layer correction approach based on two small parameters is proposed and solved. The solutions are carried out for the first and third kind of waves throughout the entire domain. The second kind of wave which disappears outside the boundary layer is solved systematically inside the boundary layer. The results are compared with the linear wave solutions of Huang and Song (Journal of Engineering Mechanics, ASCE 1993; 119:1003,1020.) to confirm the validity. Moreover, a simplified boundary layer correction formulation which is expected to be very useful in numerical computation is also proposed. Copyright © 2001 John Wiley & Sons, Ltd. [source] Numerical inclusion methods of solutions for variational inequalitiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2002C. S. Ryoo Abstract We consider a numerical method that enables us to verify the existence of solutions for variational inequalities. This method is based on the infinite dimensional fixed point theorems and explicit error estimates for finite element approximations. Using the finite element approximations and explicit a priori error estimates, we present an effective verification procedure that through numerical computation generates a set which includes the exact solution. Copyright © 2002 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] Generalization of multivariate optical computations as a method for improving the speed and precision of spectroscopic analysesJOURNAL OF CHEMOMETRICS, Issue 6 2008Marc K. Boysworth Abstract Multivariate optical computations (MOCs) offer improved analytical precision and increased speed of analysis via synchronous data collection and numerical computation with scanning spectroscopic systems. The improved precision originates in the redistribution of integration time from spurious channels to informative channels in an optimal manner for increasing the signal-to-noise ratio with multivariate analysis under the constraint of constant total analysis time. In this work, MOCs perform the multiplication and addition steps of spectral processing by adjusting the integration parameters of the optical detector or adjusting the scanning profile of the tunable optical filter. Improvement in the precision of analysis is achieved via the implicit optimization of the analytically useful signal-to-noise ratio. The speed improvements are realized through simpler data post-processing, which reduces the computation time required after data collection. Alternatively, the analysis time may be significantly truncated while still seeing an improvement in the precision of analysis, relative to competing methods. Surface plasmon resonance (SPR) spectroscopic sensors and visible reflectance spectroscopic imaging were used as test beds for assessing the performance of MOCs. MOCs were shown to reduce the standard deviation of prediction by 15% compared to digital data collection and analysis with the SPR and up to 45% for the imaging applications. Similarly, a 30% decrease in the total analysis time was realized while still seeing precision improvements. Copyright © 2008 John Wiley & Sons, Ltd. [source] Randal Heeb Innovation and Vertical Integration in Complementary MarketsJOURNAL OF ECONOMICS & MANAGEMENT STRATEGY, Issue 3 2003Randal Heeb This paper studies vertical integration by an essential-good monopolist into complementary markets. Unlike previous studies of complementary products, consumers are allowed to purchase some components of a complementary basket, but not others. Two different pricing strategies by the integrated firm may emerge. In mass-market equilibria, the price of the complement under integration is zero and it is given away with the essential good. Niche-market equilibria have more conventional pricing. This dichotomy is consistent with consumer software pricing. Integration enhances consumer and total surplus, unless it leads to exit by the higher-quality rival, in which case welfare is reduced. Exit is most likely when it is least damaging to consumer welfare. Integration reduces innovation by the rival firm. The effect on innovation by the integrated firm is ambiguous, but numerical computation of an extended model indicates that integration increases the innovation of the integrated firm and enhances welfare. [source] Computational analysis of an instantaneous chemical reaction in a T-microreactorAICHE JOURNAL, Issue 6 2010Dieter Bothe Abstract We extend and apply a method for the numerical computation of convective and diffusive mixing in liquid systems with very fast irreversible chemical reaction to the case of unequal diffusivities. This approach circumvents the solution of stiff differential equations and, hence, facilitates the direct numerical simulation of reactive flows with quasi-instantaneous reactions. The method is validated by means of a neutralization reaction which is studied in a T-shaped micromixer and compared with existing experimental LIF-data. Because of their large are-to-volume ratio, microreactors are well suited for fast chemical reactions which are seriously affected by the slow diffusive transport in aqueous media. Numerical computations for different reactor dimensions reveal the fact that, in a dimensionless setting, the obtained conversion is independent of the reactor size, if the flow conditions are the same. This corresponds to an increase of space-time-yield proportional to the square of the inverse scale factor. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] On the numerical computation of blowing-up solutions for semilinear parabolic equationsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 9 2001D. Fayyad Theoretical aspects related to the approximation of the semilinear parabolic equation: $u_t=\Delta u+f(u)$\nopagenumbers\end, with a finite unknown ,blow-up' time Tb have been studied in a previous work. Specifically, for , a small positive number, we have considered coupled systems of semilinear parabolic equations, with positive solutions and ,mass control' property, such that: \def\ve{^\varepsilon}$$u_t\ve=\Delta u\ve+f(u\ve)v\ve\qquad v_t\ve=\Delta v\ve-\varepsilon f(u\ve)v\ve$$\nopagenumbers\end The solution \def\ve{^\varepsilon}$$\{u\ve,v\ve\}$$\nopagenumbers\end of such systems is known to be global. It is shown that $$\|(u^\varepsilon-u)(\, .\, ,t)\|_\infty\leq C(M_T)\varepsilon$$\nopagenumbers\end, \def\lt{\char'74}$t\leq T \lt T_b$\nopagenumbers\end where $M_T=\|u(\, .\, ,T)\|_\infty$\nopagenumbers\end and $C(M_T)$\nopagenumbers\end is given by (6). In this paper, we suggest a numerical procedure for approaching the value of the blow-up time Tb and the blow-up solution u. For this purpose, we construct a sequence $\{M_\eta\}$\nopagenumbers\end, with $\lim_{\eta\rightarrow 0}M_\eta=\infty$\nopagenumbers\end. Correspondingly, for $\varepsilon\leq1/2C(M_\eta+1)=\eta^\alpha$\nopagenumbers\end and \def\lt{\char'74}$0\lt\alpha\lt\,\!1$\nopagenumbers\end, we associate a specific sequence of times $\{T_\varepsilon\}$\nopagenumbers\end, defined by $\|u^\varepsilon(\, .\, ,T_\varepsilon)\|_\infty=M_\eta$\nopagenumbers\end. In particular, when $\varepsilon=\eta\leq\eta^\alpha$\nopagenumbers\end, the resulting sequence $\{T_\varepsilon\equiv T_\eta\}$\nopagenumbers\end, verifies, $\|(u-u^\eta)(\, .\, ,t)\|_\infty\leq{1\over2}(\eta)^{1-\alpha}$\nopagenumbers\end, \def\lt{\char'74}$0\leq t\leq T_\eta\lt T_{\rm b}$\nopagenumbers\end with $\lim_{\eta\rightarrow 0}T_\eta=T_{\rm b}$\nopagenumbers\end. The two special cases of a single-point blow-up where $f(u)=\lambda{\rm e}^u$\nopagenumbers\end and $f(u)=u^p$\nopagenumbers\end are then studied, yielding respectively sequences $\{M_\eta\}$\nopagenumbers\end of order $O(\ln|\ln(\eta)|)$\nopagenumbers\end and $O(\{|\ln(\eta)|\}^{1/p-1})$\nopagenumbers\end. The estimate $|T_\eta-T_{\rm b}|/T_{\rm b}=O(1/|\ln(\eta)|)$\nopagenumbers\end is proven to be valid in both cases. We conduct numerical simulations that confirm our theoretical results. Copyright © 2001 John Wiley & Sons, Ltd. [source] Structured matrix methods for CAGD: an application to computing the resultant of polynomials in the Bernstein basisNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 8 2005Dario A. Bini Abstract We devise a fast fraction-free algorithm for the computation of the triangular factorization of Bernstein,Bezoutian matrices with entries over an integral domain. Our approach uses the Bareiss fraction-free variant of Gaussian elimination, suitably modified to take into account the structural properties of Bernstein,Bezoutian matrices. The algorithm can be used to solve problems in algebraic geometry that arise in computer aided geometric design and computer graphics. In particular, an example of the application of this algorithm to the numerical computation of the intersection points of two planar rational Bézier curves is presented. Copyright © 2005 John Wiley & Sons, Ltd. [source] Mathematical modeling of boundary conditions for laser-molecule time-dependent Schrödinger equations and some aspects of their numerical computation,One-dimensional caseNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2009Emmanuel Lorin Abstract This article deals with boundary conditions for time-dependent Schrödinger equations for molecules excited by intense and ultrashort electric fields. On the basis of Volkov wavefunctions, we propose an original boundary condition design that allows to reduce spurious reflections at the domain boundary and allows to take at least partially, plasma effects into account. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source] Optimised Plasma Absorption Probe for the Electron Density Determination in Reactive PlasmasPLASMA PROCESSES AND POLYMERS, Issue 1 2009Christian Scharwitz Abstract The plasma absorption probe (PAP) is a recently developed tool for the efficient determination of electron densities, especially in reactive plasmas. A dielectric cover protects this probe against the influences in reactive plasmas and it withstands conditions where Langmuir probes are easily damageable. The lack of adequate calibration constants and the occurrence of multiple absorption signals were two major drawbacks, which are successfully overcome in this work. Design variations are tested by numerical computation and the model-based achievements are established in experiment. In this work, a redesigned PAP is presented, which is optimised for the easy determination of electron densities. The developed tool works fast and efficiently, in particular in discharges in reactive gases. [source] Conserving Galerkin weak formulations for computational fracture mechanicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2002Shaofan Li Abstract In this paper, a notion of invariant Galerkin-variational weak forms is proposed. Two specific invariant variational weak forms, the J-invariant and the L-invariant, are constructed based on the corresponding conservation laws in elasticity, one of which is the conservation of Eshelby's energy-momentum (Eshelby. Philos. Trans. Roy. Soc. 1951; 87: 12; In Solid State Physics, Setitz F, Turnbull D (eds). Academic Press: New York, 1956; 331; Rice, J. Appl. Mech. 1968; 35: 379). It is shown that the finite element solution obtained from the invariant Galerkin weak formulations proposed here can conserve the value of J-integral, or L-integral exactly. In other words, the J and L integrals of the Galerkin finite element solutions are path independent in the discrete sense. It is argued that by using the J-invariant Galerkin weak form to compute near crack-tip field in an elastic solid, one may accurately calculate the crack extension energy release rate and subsequently the stress intensity factors in numerical computations, because the flux of the energy-momentum is conserved in discrete computations. This may provide an alternative means to accurately simulate crack growth and propagation. Copyright © 2002 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] Simulation of shallow flows over variable topographies using unstructured gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2006A. Mohammadian Abstract Simulation of shallow flows over variable topographies is a challenging case for most available shock-capturing schemes. This problem arises because the source terms and flux gradients are not balanced in the numerical computations. Treatments for this problem generally work well on structured grids, but they are usually too expensive, and most of them are not directly applicable to unstructured grids. In this paper we propose two efficient methods to treat the source terms without upwinding and to satisfy the compatibility condition on unstructured grids. In the first method, the calculation of the bed slope source term is performed by employing a compatible approximation of water depth at the cell interfaces. In the second one, different components of the bed slope term are considered separately and a compatible discretization of the components is proposed. The present treatments are applicable for most schemes including the Roe's method without changing the performance of the original scheme for smooth topographies. Copyright © 2006 John Wiley & Sons, Ltd. [source] Finite element modelling of free-surface flows with non-hydrostatic pressure and k,, turbulence modelINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2005C. Leupi Abstract Validation of 3D finite element model for free-surface flow is conducted using a high quality and high spatial resolution data set. The commonly numerical models with the conventional hydrostatic pressure still remain the most widely used approach for the solution of practical engineering problems. However, when a 3D description of the velocity field is required, it is useful to resort to a more accurate model in which the hydrostatic assumption is removed. The present research finds its motivation in the increasing need for efficient management of geophysical flows such as estuaries (multiphase fluid flow) or natural rivers with the presence of short waves and/or strong bathymetry gradient, and/or strong channel curvature. A numerical solution is based on the unsteady Reynolds-averaged Navier,Stokes equations on the unstructured grid. The eddy viscosity is calculated from the efficient k,, turbulence model. The model uses implicit fractional step time stepping, and the characteristics method is used to compute the convection terms in the multi-layers system (suitable for the vertical stratified fluid flow), in which the vertical grid is located at predefined heights and the number of elements in the water column depends on water depth. The bottommost and topmost elements of variable height allow a faithful representation of the bed and the time-varying free-surface, respectively. The model is applied to the 3D open channel flows of various complexity, for which experimental data are available for comparison. Computations with and without non-hydrostatic are compared for the same trench to test the validity of the conventional hydrostatic pressure assumption. Good agreement is found between numerical computations and experiments. Copyright © 2005 John Wiley & Sons, Ltd. [source] Convergence acceleration by self-adjusted time stepsize using Bi-CGSTAB method for turbulent separated flow computationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2002W. B. Tsai Abstract Poor convergence behavior is usually encountered when numerical computations on turbulent separated flow are performed. A design of self-adjusted stepsize concept both in time span and spatial coordinate systems to achieve faster convergence is demonstrated in this study. The determination of the time stepsize based on the concept of minimization of residuals using the Bi-CGSTAB algorithm is proposed. The numerical results show that the time stepsize adjusted by the proposed method indeed improves the convergence rate for turbulent separated flow computations using advanced turbulence models in low-Reynolds number forms. Copyright © 2002 John Wiley & Sons, Ltd. [source] Comparative thermal performance evaluation of an active solar distillation systemINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 15 2007G. N. Tiwari Abstract In this paper, thermal models of all types of solar collector-integrated active solar stills are developed based on basic energy balance equations in terms of inner and outer glass temperatures. In this paper, hourly yield, hourly exergy efficiency, and hourly overall thermal efficiency of active solar stills are evaluated for 0.05 m water depth. All numerical computations had been performed for a typical day in the month of 07 December 2005 for the climatic conditions of New Delhi (28°35,N, 77°12,E, 216 m above MSL). The thermal model of flat-plate collector integrated with active solar still was validated using the experimental test set-up results. Total daily yield from active solar still integrated with evacuated tube collector with heat pipe is 4.24 kg m,2 day,1, maximum among all other types of active solar stills. Copyright © 2007 John Wiley & Sons, Ltd. [source] On the asymptotic behaviour of the discrete spectrum in buckling problems for thin platesMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2006Monique Dauge Abstract We consider the buckling problem for a family of thin plates with thickness parameter ,. This involves finding the least positive multiple , of the load that makes the plate buckle, a value that can be expressed in terms of an eigenvalue problem involving a non-compact operator. We show that under certain assumptions on the load, we have , = ,,(,2). This guarantees that provided the plate is thin enough, this minimum value can be numerically approximated without the spectral pollution that is possible due to the presence of the non-compact operator. We provide numerical computations illustrating some of our theoretical results. Copyright © 2005 John Wiley & Sons, Ltd. [source] | |||||||||||||||||||||||||||||||||||||