A computational model based on an arbitrary-Lagrangian-Eulerian numerical algorithm is developed for flows separated by a free surface where the surface tension force is important. This model is used to study deformat...
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A computational model based on an arbitrary-Lagrangian-Eulerian numerical algorithm is developed for flows separated by a free surface where the surface tension force is important. This model is used to study deformation and oscillation of cylindrical/spherical droplets with and without external forced convection. The calculated frequency of droplet oscillation agrees well with the analytical value derived from perturbation analysis, and the amplitude of oscillation does not decay with time, which indicates that numerical diffusion and damping do not exist in the adopted algorithm. The deformation of an initially spherical droplet under forced convection is calculated and found consistent with the conclusions in the literature. Good agreement is also obtained in comparison with experimental results for an initially deformed droplet in forced convective flows.
High emission levels and the unfavourable topography are the main reasons for the alarming photochemical air pollution levels in Athens. An analysis of available air quality data proves that air pollution levels in At...
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High emission levels and the unfavourable topography are the main reasons for the alarming photochemical air pollution levels in Athens. An analysis of available air quality data proves that air pollution levels in Athens are largely affected by local wind circulation systems. The most frequent of these systems is dominated by the phenomenon of the sea breeze. Severe air pollution episodes occur, however, primarily under synoptic situations leading to stagnant conditions in the atmosphere over Athens. Photosmog formation in the Athens Basin is studied with the photochemical dispersion model MARS. The implicit solution algorithm incorporated in MARS is characterized by a variable time increment and a variable order. This solver allows avoiding unnecessary operator splitting by a coupled treatment of vertical diffusion and chemical kinetics. In this paper, MARS is used to analyse the situation on 25 May 1990, a day for which very high air pollution levels were reported in Athens. The simulation results elucidate the characteristics of a photosmog episode under stagnant conditions in Athens. In general, the model results reproduce satisfactorily the observed air pollution patterns.
Some numerical solutions of acoustic propagation problems using linearized Euler equations are studied. The two-dimensional Euler equations are linearized around a known stationary mean flow. The computed solution is ...
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Some numerical solutions of acoustic propagation problems using linearized Euler equations are studied. The two-dimensional Euler equations are linearized around a known stationary mean flow. The computed solution is obtained by using is dispersion-relation-preserving scheme in space, combined with a fourth-order Runge-Kutta algorithm in time. This numerical integration leads to very good results in terms of accuracy, stability, and low storage. The implementation of source terms in these equations is studied very carefully in various configurations, inasmuch as the final goal is to improve and to validate the stochastic noise generation and radiation model. In this approach, the turbulent velocity field is modeled by a sum of random Fourier modes through a source term in the linearized Euler equations to predict the noise from subsonic flows. The radiation of a point source in a subsonic and a supersonic uniform mean flow is investigated. The numerical estimates are shown to be in excellent agreement with the analytical solutions. Then, the emphasis is on the ability of the method to describe correctly the multipolar structure of aeroacoustic sources. The radiation of dipolar and guadrupolar extended sources is, thus, studied. Next, a typical problem in jet noise is considered with the propagation of acoustic waves in a sheared mean flow. The numerical solution compares favorably with ray tracing. Finally, a nonlinear formulation of Euler's equations is solved to limit the growth of instability waves excited by the acoustic source terms.
Perrin et al. (1995) and Geubelle and Rice (1995) have introduced a spectral method for numerical solution of two- and three-dimensional elastodynamic fracture problems. The method applies for ruptures confined to a p...
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Perrin et al. (1995) and Geubelle and Rice (1995) have introduced a spectral method for numerical solution of two- and three-dimensional elastodynamic fracture problems. The method applies for ruptures confined to a plane separating homogeneous elastic half spaces. In this method, the physical variables, such as the traction components of stress and displacement discontinuity on the rupture plane, are represented as Fourier series in space with time-dependent coefficients. An analytical solution is found for each Fourier mode, in that each Fourier coefficient for stress is expressed by the time convolution of the corresponding coefficient for displacement with a convolution kernel specific to the rupture mode. Once the 2D formulation of the method is known, the method is readily generalizable to 3D problems in that it involves only linear combinations of the convolution kernels found for each rupture mode in 2D. This conceptual simplicity has, however, a major drawback: due to the Fourier series representations of the physical variables, the problem solved is in fact an infinite and periodic replication of rupture events on the fracture plane. So, in order to study the evolution of a single rupture, one has to use a spatial period large enough in order that the waves coming from the replication cracks do not enter the zone of interest during the time duration studied, or provide negligible stress alteration when they do arrive. We show here how to rigorously offset this defect while retaining the modal independence. Once expressed in the spatial domain, the method amounts to truncating in space the space-time convolution kernels, in a manner that provides an exact evaluation for all positions within the rupture domain (where the constitutive law between stress and displacement discontinuity is to be imposed), but not outside. In order for the method to be identical in structure to the method of Perrin er al. (1995) and Geubelle and Rice (1995), the period of the Fou
A numerical algorithm for calculating the generalized Mittag-Leffler E alpha, beta(z) function for arbitrary complex argument z and real parameters alpha > 0 and beta is an element of R is presented. The algorithm ...
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A numerical algorithm for calculating the generalized Mittag-Leffler E alpha, beta(z) function for arbitrary complex argument z and real parameters alpha > 0 and beta is an element of R is presented. The algorithm uses the Taylor series, the exponentially improved asymptotic series, and integral representations to obtain optimal stability and accuracy of the algorithm. Special care is applied to the limits of validity of the different schemes to avoid instabilities in the algorithm.
Markov reward models have interesting modeling applications, particularly those addressing fault-tolerant hardware/software systems. In this paper, we consider a Markov reward model with a reward structure including o...
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Markov reward models have interesting modeling applications, particularly those addressing fault-tolerant hardware/software systems. In this paper, we consider a Markov reward model with a reward structure including only reward rates associated with states, in which both positive and negative reward rates are present and null reward rates are allowed, and develop a numerical method to compute the distribution function of the cumulative reward till exit of a subset of transient states of the model. The method combines a model transformation step with the solution of the transformed model using a randomization construction with two randomization rates. The method introduces a truncation error, but that error is strictly bounded from above by a user-specified error control parameter. Further, the method is numerically stable and takes advantage of the sparsity of the infinitesimal generator of the transformed model. Using a Markov reward model of a fault-tolerant hardware/software system, we illustrate the application of the method and analyze its computational cost. Also, we compare the computational cost of the method with that of the (only) previously available method for the problem. Our numerical experiments seem to indicate that the new method can be efficient and that for medium size and large models can be substantially faster than the previously available method.
We consider the changing face of computing and the evolving interface of numerical algorithms from subroutines to: spreadsheets, high-level scripting languages, visual programming, Web browsers. Through examples we co...
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We consider the changing face of computing and the evolving interface of numerical algorithms from subroutines to: spreadsheets, high-level scripting languages, visual programming, Web browsers. Through examples we consider the movement from the subroutine language interface to sophisticated computational environments and trace how NAG libraries and products have evolved along this path. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.
Phase change problems are of practical importance and can be found in a wide range of engineering applications. In the present paper, two proposed numerical algorithms are developed;the first one is general for phase ...
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Phase change problems are of practical importance and can be found in a wide range of engineering applications. In the present paper, two proposed numerical algorithms are developed;the first one is general for phase change problems, while the second one is for ablation problems. The boundary elements method is used as a mathematical tool in conjunction with the proposed algorithms. Two test examples were solved and the results agree with the physics of the problems. (C) 2009 Elsevier Ltd. All rights reserved.
The authors present a numerical method for determining a dynamic output feedback controller. Such a controller has the capability of stabilizing systems where static output feedback fails while being simpler in struct...
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The authors present a numerical method for determining a dynamic output feedback controller. Such a controller has the capability of stabilizing systems where static output feedback fails while being simpler in structure than the control based on the separation theorem, where one first designs the controller gains assuming the complete state can be measured and then uses the same gains with an estimated state. The procedure is extended to the problem of simultaneously stabilizing several plants by a single controller.
A new scheme for numerical integration of motion for classical systems composed of rigid polyatomic molecules is proposed. The scheme is based on a matrix representation of the rotational degrees of freedom. The equat...
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A new scheme for numerical integration of motion for classical systems composed of rigid polyatomic molecules is proposed. The scheme is based on a matrix representation of the rotational degrees of freedom. The equations of motion are integrated within the Verlet framework in velocity form. It is shown that, contrary to previous methods, in the approach introduced the rigidity of molecules can be conserved automatically without any additional transformations. A comparison of various techniques with respect to numerical stability is made. (C) 1998 Published by Elsevier Science B.V.
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