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Numerical Solution Of The Equations Of The One Parameter Boundary Layer Theory
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Book Synopsis Numerical Solution of the Equations of the 'one-parameter' Boundary-layer Theory by : L. M. Simuni
Download or read book Numerical Solution of the Equations of the 'one-parameter' Boundary-layer Theory written by L. M. Simuni and published by . This book was released on 1966 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: The parameter method of Loitsyanskii is applied to numerical solution of a universal partial differential boundary-layer equation containing only one form parameter. Initial conditions for integration are the stream function values obtained by Loitsyanskii in the vicinity of the regular singular point of the equation. Introduction of stream velocity components leads to a system of partial differential equations with boundary conditions which is similar to the coventional boundary-layer equations and is solved by a finite-difference method. The procedure of solution, the formulas for calculating the values of the velocity components and stream function, and the computational technique are given. The accuracy of the calculation near the singular point was checked by comparing the results of numerical integration with those obtained by series expansion. Coincidence up to the fourth significant digit was obtained in the first steps. (Author).
Book Synopsis Numerical Solution of Equations in the Two Parameter Theory of the Boundary Layer by : E. F. Ozerova
Download or read book Numerical Solution of Equations in the Two Parameter Theory of the Boundary Layer written by E. F. Ozerova and published by . This book was released on 1972 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper presents a numerical solution of problems of the parametric boundary layer theory in a two-parameter approximation. The partial differential boundary layer equation is solved by a finite difference method using an implicit difference scheme, and the results obtained serve as the initial data. The derivatives in the original equation are replaced by finite difference equations, and the resulting system is solved by a brute force method. A table lists the numerical results obtained by computer.
Book Synopsis Numerical Solution of Nonlinear Boundary Value Problems with Applications by : Milan Kubicek
Download or read book Numerical Solution of Nonlinear Boundary Value Problems with Applications written by Milan Kubicek and published by Courier Corporation. This book was released on 2008-01-01 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of the development, analysis, and application of numerical techniques in solving nonlinear boundary value problems, this text presents numerical analysis as a working tool for physicists and engineers. Starting with a survey of accomplishments in the field, it explores initial and boundary value problems for ordinary differential equations, linear boundary value problems, and the numerical realization of parametric studies in nonlinear boundary value problems. The authors--Milan Kubicek, Professor at the Prague Institute of Chemical Technology, and Vladimir Hlavacek, Professor at the University of Buffalo--emphasize the description and straightforward application of numerical techniques rather than underlying theory. This approach reflects their extensive experience with the application of diverse numerical algorithms.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1975 with total page 970 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Book Synopsis Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations by : A.K. Aziz
Download or read book Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations written by A.K. Aziz and published by Academic Press. This book was released on 2014-05-10 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations covers the proceedings of the 1974 Symposium by the same title, held at the University of Maryland, Baltimore Country Campus. This symposium aims to bring together a number of numerical analysis involved in research in both theoretical and practical aspects of this field. This text is organized into three parts encompassing 15 chapters. Part I reviews the initial and boundary value problems. Part II explores a large number of important results of both theoretical and practical nature of the field, including discussions of the smooth and local interpolant with small K-th derivative, the occurrence and solution of boundary value reaction systems, the posteriori error estimates, and boundary problem solvers for first order systems based on deferred corrections. Part III highlights the practical applications of the boundary value problems, specifically a high-order finite-difference method for the solution of two-point boundary-value problems on a uniform mesh. This book will prove useful to mathematicians, engineers, and physicists.
Book Synopsis Boundary-Layer Theory by : Hermann Schlichting (Deceased)
Download or read book Boundary-Layer Theory written by Hermann Schlichting (Deceased) and published by Springer. This book was released on 2016-10-04 with total page 814 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition of the near-legendary textbook by Schlichting and revised by Gersten presents a comprehensive overview of boundary-layer theory and its application to all areas of fluid mechanics, with particular emphasis on the flow past bodies (e.g. aircraft aerodynamics). The new edition features an updated reference list and over 100 additional changes throughout the book, reflecting the latest advances on the subject.
Book Synopsis Numerical Solution of the Equations for Compressible Laminar, Transitional, and Turbulent Boundary Layers and Comparisons with Experimental Data by : Julius E. Harris
Download or read book Numerical Solution of the Equations for Compressible Laminar, Transitional, and Turbulent Boundary Layers and Comparisons with Experimental Data written by Julius E. Harris and published by . This book was released on 1971 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: A numerical method for solving the equations for laminar, transitional, and turbulent compressible boundary layers for either planar or axisymmetric flows is presented. The fully developed turbulent region is treated by replacing the Reynolds stress terms with an eddy viscosity model. The mean properties of the transitional boundary layer are calculated by multiplying the eddy viscosity by an intermittency function based on the statistical production and growth of the turbulent spots. A specifiable turbulent Prandtl number relates the turbulent flux of heat to the eddy viscosity. A three-point implicit finite-difference scheme is used to solve the system of equations. The momentum and energy equations are solved simultaneously without iteration. Numerous test cases are compared with experimental data for supersonic and hypersonic flows; these cases include flows with both favorable and mildly unfavorable pressure gradient histories, mass flux at the wall, and traverse curvature.
Book Synopsis A Parametric Method of Integrating Laminar-boundary Layer Equations by : Victor Klein
Download or read book A Parametric Method of Integrating Laminar-boundary Layer Equations written by Victor Klein and published by . This book was released on 1966 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: The article is divided into four parts: (1) The universal equation of the laminar boundary layer; (2) One-parameter solution; (3) Representation of the solution in the form of a series in powers of formparameters; (4) An example of calculating a boundary layer. Conclusion. A new method for solving the problems in the theory of the laminar boundary layer is presented. The fundamental equations of a two-dimensional isothermal laminar boundary layer are reduced to a 'universal' partial differential equation in terms of a reduced stream function containing certain boundary-layer parameters (called 'formparameters'), which express the influence of the velocity profile at the outer interface of the boundary layer on its characteristics. The numerical integration of the universal equation is carried out once and for all and is followed by a tabulation of the stream function, the skin-friction factor, and other characteristic quantities. These tables can be used to determine the required parameters for any other particular boundary-layer problem (after deriving a universal equation for it) by relatively simple calculations which do not require the use of electronic computers. (Author).
Book Synopsis Fitted Numerical Methods For Singular Perturbation Problems: Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions by : John J H Miller
Download or read book Fitted Numerical Methods For Singular Perturbation Problems: Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions written by John J H Miller and published by World Scientific. This book was released on 1996-01-01 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the first edition of this book the literature on fitted mesh methods for singularly perturbed problems has expanded significantly. Over the intervening years, fitted meshes have been shown to be effective for an extensive set of singularly perturbed partial differential equations. In this revised version of this book, the reader will find an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. The global errors in the numerical approximations are measured in the pointwise maximum norm. The fitted mesh algorithm is particularly simple to implement in practice, but the theory of why these numerical methods work is far from simple. This book can be used as an introductory text to the theory underpinning fitted mesh methods.
Book Synopsis Numerical Solution of Two Point Boundary Value Problems by : Herbert B. Keller
Download or read book Numerical Solution of Two Point Boundary Value Problems written by Herbert B. Keller and published by SIAM. This book was released on 1976-01-01 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lectures on a unified theory of and practical procedures for the numerical solution of very general classes of linear and nonlinear two point boundary-value problems.
Book Synopsis Integral Methods in the Theory of the Boundary Layer by : Lev Gerasimovich Loĭt͡si͡anskiĭ
Download or read book Integral Methods in the Theory of the Boundary Layer written by Lev Gerasimovich Loĭt͡si͡anskiĭ and published by . This book was released on 1944 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: The application of the well-known basic principle of mechanics, the principle of Jourdain, to problems of the theory of the boundary layer leads to an equation from which the equations of Von Karman, Leibenson, and Golubev are derived as special cases. The given equation may be employed in other integral methods. The present paper deals with the method of the variation of the thickness of the boundary layer. A number of new approximate formulas valuable in aerodynamic calculations for the fristion distribution are derived from this procedure. The method has been applied only to laminar boundary layers, but it seems probable that it may be generalized to include turbulent layers as well.
Book Synopsis Numerical Solution of the Navier-Stokes Equations for a Shock-boundary Layer Interaction Problem Using an L-U Implicit Scheme by : Juichi Nagano
Download or read book Numerical Solution of the Navier-Stokes Equations for a Shock-boundary Layer Interaction Problem Using an L-U Implicit Scheme written by Juichi Nagano and published by . This book was released on 1984 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Technical Abstract Bulletin by : Defense Documentation Center (U.S.)
Download or read book Technical Abstract Bulletin written by Defense Documentation Center (U.S.) and published by . This book was released on 1964 with total page 1148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Fast Solution of Boundary Integral Equations by : Sergej Rjasanow
Download or read book The Fast Solution of Boundary Integral Equations written by Sergej Rjasanow and published by Springer Science & Business Media. This book was released on 2007-04-17 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed description of fast boundary element methods, all based on rigorous mathematical analysis. In particular, the authors use a symmetric formulation of boundary integral equations as well as discussing Galerkin discretisation. All the necessary related stability and error estimates are derived. The authors therefore describe the Adaptive Cross Approximation Algorithm, starting from the basic ideas and proceeding to their practical realization. Numerous examples representing standard problems are given.
Book Synopsis Numerical Method for the Solution of Large Systems of Differential Equations of the Boundary-layer Type by : Michael J. Green (Environmental engineer)
Download or read book Numerical Method for the Solution of Large Systems of Differential Equations of the Boundary-layer Type written by Michael J. Green (Environmental engineer) and published by . This book was released on 1972 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: A numerical method for the solution of large systems of nonlinear differential equations of the boundary-layer type is described. The method is a modification of the technique for satisfying asymptotic boundary conditions. The present method employs inverse interpolation instead of the Newton method to adjust the initial conditions of the related initial-value problem. This eliminates the so-called perturbation equations. The elimination of the perturbation equations not only reduces the user's preliminary work in the application of the method, but also reduces the number of time-consuming initial-value problems to be numerically solved at each iteration. For further ease of application, the solution of the overdetermined system for the unknown initial conditions is obtained automatically by applying Golub's linear least-squares algorithm. The relative ease of application of the proposed numerical method increases directly as the order of the differential-equation system increases. Hence, the method is especially attractive for the solution of large-order systems. After the method is described, it is applied to a fifth-order problem from boundary-layer theory.
Book Synopsis Numerical Solution of the Compressible Boundary Layer Equations Over Axisymmetric Surfaces by : Charles R. Blake
Download or read book Numerical Solution of the Compressible Boundary Layer Equations Over Axisymmetric Surfaces written by Charles R. Blake and published by . This book was released on 1976 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: A numerical solution of the compressible boundary layer equations was developed for flows over either two-dimensional or axisymmetric surfaces. The solution method is capable of solving for boundary layer parameters in either laminar or turbulent flows. In the case of turbulent flow, closure is achieved by use of a two-layered eddy viscosity model. The boundary layer equations are solved by a numerical marching procedure. A Mangler-Levy-Lees transformation of independent variables is used to improve the efficiency of the numerical solution. The transformed boundary layer equations are then linearized by a three point finite difference scheme. The linearized equations are solved by a matrix solution technique. Comparisons of computed boundary layer parameters with experimentally determined parameters were made for both laminar and turbulent flows over axisymmetric bodies. The comparisons show the numerical solution to be very accurate. (Author).
Book Synopsis On the Convergence and Exactness of Solutions of the Laminar Boundary-layer Equations Using the N-parameter Integral Formulation of Galerkin-kantorovich-dorodnitsyn by : Howard E. Bethel
Download or read book On the Convergence and Exactness of Solutions of the Laminar Boundary-layer Equations Using the N-parameter Integral Formulation of Galerkin-kantorovich-dorodnitsyn written by Howard E. Bethel and published by . This book was released on 1966 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: The solution of the incompressible, laminar boundary-layer equations using the N-parameter integral method of Galerkin, Kantorovich and Dorodnitsyn is investigated. This method seeks to obtain an approximate solution of a partial differential equation with given boundary conditions by assuming the solution in functional form so that the boundary conditions for one variable are exactly satisfied. The approximating function is then specialized in such a manner as to obtain approximate satisfaction of the given equation. Solutions are presented for the similar flows and four types of nonsimilar flows: flows with an abrupt change from an initial region of flow to a constant velocity flow, analytically prescribed external flows, experimentally determined external flows, and flows which proceed from a stagnation point to a separation point. These results indicate that the GKD method yields solutions which are uniformly better than classical approximation techniques and are of about the same accuracy as the usual 'exact' numerical solution methods such as the series method, the Hartree-Womersley method and finite difference methods. Furthermore, solutions can be obtained as close to the separation point as computationally feasible. (Author).
