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Finite Difference Methods of Solution of Nonlinear Flow Processes with Application to the Ben©Øard Problem

Author : Jacob E. Fromm

Publisher :

Page : 138 pages

File Size : 29,87 MB

Release : 1966

Category : Finite differences

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Book Description

A general method of numerical calculation of compressible flows is outlined in which such flows are divided into irrotational and solenoidal parts. The general equations are reduced to the Boussinesq approximation for consideration of the B©Øenard problem. The B©Øenard problem, both in method of solution and result, is used to analyse a number of crucial aspects of finite difference calculation. In particular, the nonlinear formulations in current use are developed and related in a systematic way; and, in addition, some higher order methods are derived. Examples of the time-dependent behavior of the thermal convection problem are examined for physical interpretation in terms of gross property measurements and character of instantaneous solutions with the hope that the experience so gained will be valuable to extensions of the numerical method to more general problems.





Computation of Three-Dimensional Transonic Internal Flow in Cylindrical Coordinates

Author : W. J. Phares

Publisher :

Page : 35 pages

File Size : 15,42 MB

Release : 1981

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ISBN :

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Book Description

The Euler equations for the inviscid rotational flow of a perfect gas are solved for three-dimensional subsonic-transonic internal flow by use of a time-dependent numerical technique. The numerical approach, which is an extension and modification of that of Cline for two-dimensional flows, is based on the use of the MacCormack finite-difference method for the interior field points. The reference-plane method of characteristics is used for coupling the interior field solution to the boundary points. Both the basic equations and the numerical procedures are described, as is the computer program which was written in FORTRAN IV language for either the Cray-1 or the IBM 370/165 computer. As presently written, the program is applicable to the computation of three-dimensional flow in both axisymmetric and relatively simple three-dimensional nozzle geometries. The validity of the computer program was established by computing, in various ways, an axisymmetric nozzle flow as a three-dimensional flow; the numerical results are in good agreement with the results from a well-established computer program for axisymmetric flow. (Author).