Analytical approximate solutions for two-dimensional incompressible Navier-Stokes equations

Analytical approximate solutions of the two-dimensional incompressible Navier-Stokes equations by means of Adomian decomposition method are presented. The power of this manageable method is confirmed by applying it for two selected  flow problems: The first is the Taylor decaying vortices, and the second is the flow behind a grid, comparison with High-order upwind compact finite-difference method is made. The numerical results that are obtained for two incompressible flow problems  showed that the proposed method is less time consuming, quite accurate and easily implemented. In addition, we prove the convergence of this method when it is applied to the flow problems, which are describing them by  unsteady two-dimensional incompressible Navier-Stokes equations.   Keywords: Navier-Stokes equations, Adomian decomposition, upwind compact difference, Accuracy, Convergence analysis,Taylor's decay vortices, flow behind a grid

Preconditioners for the spectral multigrid method

The systems of algebraic equations which arise from spectral discretizations of elliptic equations are full and direct solutions of them are rarely feasible. Iterative methods are an attractive alternative because Fourier transform techniques enable the discrete matrix-vector products to be computed with nearly the same efficiency as is possible for corresponding but sparse finite difference discretizations. For realistic Dirichlet problems preconditioning is essential for acceptable convergence rates. A brief description of Chebyshev spectral approximations and spectral multigrid methods for elliptic problems is given. A survey of preconditioners for Dirichlet problems based on second-order finite difference methods is made. New preconditioning techniques based on higher order finite differences and on the spectral matrix itself are presented. The preconditioners are analyzed in terms of their spectra and numerical examples are presented

A boundary integral method for an inverse problem in thermal imaging

An inverse problem in thermal imaging involving the recovery of a void in a material from its surface temperature response to external heating is examined. Uniqueness and continuous dependence results for the inverse problem are demonstrated, and a numerical method for its solution is developed. This method is based on an optimization approach, coupled with a boundary integral equation formulation of the forward heat conduction problem. Some convergence results for the method are proved, and several examples are presented using computationally generated data

Solution of First-Order Differential Equation Using Fourth-Order Runge-Kutta Approachand Adams Bashforth Methods

In this research, we investigate the solution of first-order differential equations(DEs) using Runge- Kutta fourth-order method (RKM) and Adams-Bashforth methods (ABMs). In this work we considerfourth-order RKM and ABMs for solving first order DEs. The method proof to be simple, easy, accurate and efficient technique for solving first order DEs. Moreover, there are unlimited application of fourth-order RK4 and ABMs for solving first-order DE in science, engineering, economics, social science, biology and business. These play an important role in science and engineering. Some examples are giving and solved to support the efficiency of our methods which are demonstrated by figures

Solution of First-Order Differential Equation Using Fourth-Order Runge-Kutta Approach and Adams Bashforth Methods

In this research, we investigate the solution of first-order differential equations (DEs) using Runge- Kutta fourth-order method (RKM) and Adams-Bashforth methods (ABMs). In this work we consider fourth-order RKM and ABMs for solving first order DEs. The method proof to be simple, easy, accurate and efficient technique for solving first order DEs. Moreover, there are unlimited application of fourth-order RK4 and ABMs for solving first-order DE in science, engineering, economics, social science, biology and business. These play an important role in science and engineering. Some examples are giving and solved to support the efficiency of our methods which are demonstrated by figures. &nbsp

Characterization of the Turbulent Structure in Compound Channel Flows

The main goal of this investigation is to characterize the turbulent structures in compound channel flows considering two geometrical conditions, a simple asymmetric compound channel and the same compound channel but with the placement of rods on the upper bank. For the simple asymmetric compound channel, three different water depths were analyzed, one corresponding to deep flows and two corresponding to shallow flows. For the compound channel with rods, three different spacing between elements were studied, including two different water depths for each spacing condition. The measurements were taken with a 2D Laser Doppler Velocimiter, at 9.0 m from the inlet for simple compound channel. For the compound channel with rods, three cross-section around 9.0 m from the inlet of the channel were measured, corresponding to locations downstream of the rod, in the middle of two rods and upstream of the rod. The measurements were performed under quasi-uniform flow condition and streamwise and vertical instantaneous velocity components were obtained. The raw data was filtered and processed in order to estimate the time-averaged velocities U and W, the turbulent intensities U' and W', Reynolds stress u'w' , streamwise integral length scale Lx, turbulence dissipation rate ε and Taylor’s micro scale x. Taylor's frozen field hypothesis was adopted in order to transform the time record into a space record, using a convection velocity Uc. The autocorrelation function was built and the integral length scale estimated using three different stop methods of the integral: the second zero of the autocorrelation function, the first minimum, and assuming the integral length scale as the wavenumber value when the autocorrelation function reaches 1/e (this was concluded to be the most consistent method). For estimating the dissipation rate, the following methods were used: from the third order structure function, from the second order structure function and finally, and from the energy spectrum of the velocity (this was concluded to be the most consistent method). In the case of a simple compound channel, the deep flows are characterized by macro vortices with streamwise axis between the interface and main channel and between interface and floodplain, having a notable separation in the "main channel vortex" and the "floodplain vortex" meeting, due the double shear layer of the streamwise depth-averaged velocity. Shallow flows are characterized by macro vortices with vertical axis confined between the interface and main channel and originated by the depth average velocity gradient between the main channel and floodplain. A clear linear relation exists between the streamwise integral length scale, Lx, the dissipation rate, ε, and the streamwise turbulent intensity U’. Contrary to 2D fully developed open-channel flow equations that relation appears to be constant for all water depths. For the compound channel with rods, new turbulent structures are generated due the interaction between rods and flow. Downstream of rods, the horseshoes-vortex system is perfectly observed and a strong descendant flow dominate both sides of rod, turning invalid the universal laws for 2D fully developed open-channel flows. The integral length scale presents almost constant values in the vertical direction, which indicates that the wakes generated by the rods influence the entire water column. The turbulent microscale and dissipation rate acquire a streamwise variation due to the vortex propagation in the downstream direction, both presenting higher values than the ones corresponding to 2D flows

The Canada-U.S. Auto Pact of 1965: An Experiment in Selective Trade Liberalization

In this paper we analyse the Canada-U.S. Auto Pact, a selective trade liberalization agreement which created a duty-free North American market for the major U.S. multinational automobile producers, but continued to protect them from offshore producers. The new international trade/I.O. literature predicts that, given the probable unexploited economics of scale and specialization in the tariff-protected small Canadian economy prior to 1965, rationalization leading to large efficiency gains in Canadian production vis a vis U.S. production would occur in a free trade environment. We estimate that the Auto Pact did not induce a substantial improvement in Canadian relative production efficiency. The missing ingredient seems to have been the competition-increasing effects of free trade in an oligopolistic setting that is emphasized by the new trade/I.O. literature. The Auto Pact did not increase the number of rivals in the oligopolistic Canadian industry since the major players in the industry had production facilities on both sides of the Canada-U.S. border before 1965, and no significant new entry into Canada occurred. In the 1962-64 period, Canadian automotive production was 27% less efficient than U.S. production. By 1970-72 this deficiency had been reduced to 19%, but was not further reduced by the end of the 1970's. Of the 8 percentage points reduction in the Canadian disadvantage, we attribute only 3 percentage points to the rationalization process induced specifically by the Auto Pact.

The Turbulent Transport and Biological Structure of Eutrophication Models. Volume I: Preserving the Statistical Structure in Lake Transport Calculations

Project Completion Report, Volume I Office of Water Resources Research and Technology Matching Grant B-O36-OHIO(print) v. ; ill. ; 28 cm.Preface -- Acknowledgments -- List of Tables -- List of Figures -- List of Symbols -- Chapter I. Introduction and Objective -- Chapter II. Review of Turbulent Transport Models -- Chapter III. Turbulence -- Chapter IV. Filtration -- Chapter V. Derivation of Filtered Transport Equations -- Chapter VI. Numerical Solution -- Chapter VII. Model Implementation -- Chapter VIII. Results -- Chapter IX. Interpretation and Discussion -- Chapter X. Conclusions -- Appendix -- Reference

An Exploration into the Determinants of Research Intensity

This paper explores the economic factors which determine the variation of research effort across firms. The intra-industry coefficient of variation of research intensity is much larger than those of traditional factors. We show that this important fact is consistent with the theoretical argument that knowledge possesses unique economic characteristics, and that the demand for research depends both on the parameters of the production function for knowledge and on the ability of the firm to appropriate the benefits from the knowledge it produces. We propose and implement a framework for decomposing the observed intra-industry variance In research intensity into three components: demand inducement, a firm-specific structural parameter, and errors in the observed variables. The main empirical findings are that errors in the variables (especially research) are important, that very little of the structural variance in research intensity is accounted for by demand inducement, and that the bulk of the variance is related to differences in the firm-specific parameter. Both the theoretical and empirical analysis indicate that it is not reasonable to treat the demand for research in a manner analogous to the demand for traditional inputs, including capital. Substantially richer models are required to provide insight into the structure of incentives driving the demand for research.