A Second-Order Numerical Method of Characteristics for Three-Dimensional Supersonic Flow. Volume 1. Theoretical Development and Results

A general numerical method of characteristics applicable to problems in magneto-fluid dynamics as well as ordinary fluid dynamics is described. The method can be applied to unsteady three-dimensional flows of chemically reacting, non-equilibrium, multi-component media. Dissipative phenomena must be neglected in order to make the governing equations of change hyperbolic, because the method can be applied only to quasi-linear, hyperbolic, partial differential equations. Practical restrictions on computation time usually require unsteady problems to be limited to cases with short transient times although theoretically the method applies to all unsteady flows. In steady flow the local velocity must be greater than the largest local wave speed. The characteristic and compatibility equations are derived for the most general case of magnetofluid dynamics. A new finite-difference network and its corresponding equations are developed similarly. Specialization of the general method to consider simpler problems is outlined. Preliminary numerical results of calculations using the method are presented. The practicality and feasibility of utilizing the general numerical method of characteristics on presently available, electronic digital computers is evaluated in the light of recent experience in calculating multi-dimensional flows with the method.

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Method of Characteristics for supersonic flow of a guiding centre plasma

Journal of Plasma Physics ◽

10.1017/s0022377800006425 ◽

1972 ◽

Vol 7 (1) ◽

pp. 87-98 ◽

Cited By ~ 1

Author(s):

Y. C. Whang

Keyword(s):

Supersonic Flow ◽

Acoustic Waves ◽

Method Of Characteristics ◽

Three Dimensional ◽

Oblate Spheroid ◽

The Moon ◽

Characteristic Theory ◽

Analytic Expression ◽

Field Lines ◽

Macroscopic Equations

A study of the compressive magneto-acoustic waves in a guiding centre plasma shows that the wave-front that emerges from a point disturbance after a finite time is a simple oblate spheroid with the axis of revolution parallel to the field lines. Thus, in a steady three-dimensional supersonic flow of guiding centre plasma a simple analytic expression can be obtained to represent the characteristic surfaces. From a proper linear combination of the governing macroscopic equations, the characteristic equation is obtained. It represents the propagation of disturbances on the characteristic surface. The characteristic theory can be used to study the interaction of the solar wind with the moon and possibly with other planetary bodies.

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Linearized Solutions for the Supersonic Flow Through Turbomachinery Blade Rows (Using Actuator Disk Theory)

Journal of Fluids Engineering ◽

10.1115/1.3240690 ◽

1980 ◽

Vol 102 (3) ◽

pp. 330-337

Author(s):

J. H. Horlock ◽

C. F. Grainger

Keyword(s):

Supersonic Flow ◽

Method Of Characteristics ◽

Three Dimensional ◽

Actuator Disk ◽

Blade Row ◽

Flow Through ◽

Twisted Blade ◽

Disk Method

An actuator disk method is developed for calculating the flow through the blade rows of a turbomachine in which the velocity relative to the blading may be supersonic. The method is compared with calculations of the fully supersonic flow through a twisted blade row using a three-dimensional method of characteristics.

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Spatial Supersonic Flow Through Annular Cascades

Journal of Engineering for Power ◽

10.1115/1.3446163 ◽

1976 ◽

Vol 98 (2) ◽

pp. 274-280

Author(s):

H. H. Fruehauf

Keyword(s):

Supersonic Flow ◽

Approximation Method ◽

Method Of Characteristics ◽

Three Dimensional ◽

Dimensional Approximation ◽

Practical Design ◽

Dynamical Parameters ◽

Flow Through ◽

Guiding Principles

The spatial supersonic flow through rotating and stationary annular cascades is analyzed by means of a nonlinear three-dimensional method of characteristics. Three-dimensional corrections for flow quantities referred to a quasi-three-dimensional approximation method are determined depending on geometric and gas dynamical parameters. Characteristic properties of spatial supersonic flow through annular cascades are analyzed, leading to guiding principles for practical design purposes.

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The method of characteristics for steady supersonic rotational flow in three dimensions

Journal of Fluid Mechanics ◽

10.1017/s0022112056000251 ◽

1956 ◽

Vol 1 (4) ◽

pp. 409-423 ◽

Cited By ~ 25

Author(s):

Maurice Holt

Keyword(s):

Supersonic Flow ◽

Method Of Characteristics ◽

Equations Of Motion ◽

Three Dimensional ◽

Three Dimensions ◽

Rotational Flow ◽

Conical Flow ◽

Plane Flow ◽

Flow Problems ◽

The Method Of Characteristics

The method of characteristics for steady supersonic flow problems in three dimensions, due to Coburn & Dolph (1949), is extended so that flow with shocks and entropy changes may be treated. Equations of motion based on Coburn & Dolph's characteristic coordinate system are derived and a scheme is described for solving these by finite differences.A linearized method of characteristics is developed for calculating perturbations of a given three-dimensional field of flow. This is a generalization of the method evolved by Ferri (1952) for perturbations of plane flow and conical flow.

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