Least Squares Finite Element Simulation of Transonic Flows PDF Download
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Author: T. F. Chen
Publisher:
ISBN:
Category :
Languages : en
Pages : 36
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Book Description
Author: T. F. Chen
Publisher:
ISBN:
Category :
Languages : en
Pages : 36
Get Book Here
Book Description
Author: T. F. Chen
Publisher:
ISBN:
Category :
Languages : en
Pages : 36
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Book Description
Author: S. T. K. Chan
Publisher:
ISBN:
Category : Aerodynamics, Transonic
Languages : en
Pages : 26
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Book Description
Author: Bo-nan Jiang
Publisher: Springer Science & Business Media
ISBN: 3662037408
Category : Science
Languages : en
Pages : 425
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Book Description
This is the first monograph on the subject, providing a comprehensive introduction to the LSFEM method for numerical solution of PDEs. LSFEM is simple, efficient and robust, and can solve a wide range of problems in fluid dynamics and electromagnetics.
Author: H. C. Chen
Publisher:
ISBN:
Category :
Languages : en
Pages : 112
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Book Description
A finite element program is described for computing steady and unsteady (oscillatory and transient) transonic flows over thin airfoils by solving directly the unsteady, nonlinear transonic potential equation based on small disturbance theory. The present numerical algorithm is developed using the concept of finite elements in conjunction with the least squares method of weighted residuals applied to both space and time. The basic element presently used is a product of an element in space and an element in time. The former has a cubic expansion inside each element, while the latter is a quadratic Lagrangian element. For each time step, the finite element discretization in both space and time results in a recurrence relationship in the form of a banded system of algebraic equations, which is solved by Gaussian elimination. The embedded shocks are smeared and a matching scheme for computing effectively flow over lifting airfoils is also incorporated in the program. The present computer program is composed of two parts: the first part (designated as UTRANL-I) generates, from a limited number of input cards, the necessary mesh information and, if desired, produces a CALCOMP mesh plot; the second part (UTRANL-II) carries out the analysis and displays the pressure coefficients along the chordline on printer plots. Two sample cases of flow over a NACA 64A 410 and a NACA 64A 006 airfoils are given to demonstrate the applicability and usage of the program. Te solution procedures are found to be quite efficient and accurate, permitting the aerodynamic forces to be calculated to engineering accuracy in less than ten minutes CPU time on a CDC 6600 computer for the most time consuming case among all those studied. (Author).
Author: S. T. K. Chan
Publisher:
ISBN:
Category : Aerodynamics, Transonic
Languages : en
Pages : 26
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Book Description
Author: United States. National Aeronautics and Space Administration. Scientific and Technical Information Office
Publisher:
ISBN:
Category : Aerodynamics, Transonic
Languages : en
Pages : 142
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Book Description
Author: Aspi Rustom Wadia
Publisher:
ISBN:
Category : Finite element method
Languages : en
Pages : 120
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Book Description
Author: S. T. K. Chan
Publisher:
ISBN:
Category :
Languages : en
Pages : 69
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Book Description
A finite element algorithm is described for computing steady and unsteady (oscillatory and transient) transonic flows over thin airfoils by solving directly the unsteady, nonlinear transonic potential equation based on small disturbance theory. The numerical algorithm is developed using the concept of finite elements in conjunction with the least squares method of weighted residuals applied to both space and time. The basic element presently used is a product of an element in space and an element in time. The former has a cubic expansion inside each element, while the latter is a quadratic Lagrange element. The embedded shocks are smeared and, in computing flow over lifting airfoils, use is made of the far field asymptotic solution to increase computational efficiency. For each time step, the finite element discretization in both space and time results in a recurrence relationship in the form of a banded system of algebraic equations, which is solved by Gaussian eliminations. Sample problems of steady flow over lifting airfoils and unsteady flow over airfoils executing harmonic motion are calculated to demonstrate the applicability and validity of the present approach. The solution procedures are found to be adequately accurate and very efficient, with unsteady solution obtainable in less than ten minutes CPU time on a CDC 6600 computer. (Author).
Author: Aspi Rustom Wadia
Publisher:
ISBN:
Category :
Languages : en
Pages : 12
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Book Description
The governing differential equation for the one-dimensional, transonic flow in a laval nozzle in the vicinity of the throat was obtained in the non-dimensional form. A least square finite element technique was used with a linearly interpolating polynomial to reduce the governing equation to a system of non-linear algebraic equations which were solved numerically by Newton's method. The system of partial differential equations for the two dimensional flow in a laval nozzle was also obtained in the non-dimensional form. The method of integral relations was used to replace the original system of partial differential equations by a system of ordinary differential equations. Using the least square finite element technique a computer program was developed for the construction and solution of the non-linear equations for the laval nozzle problem. The results including the location of the shock in the flow are presented. (Author).
