Abstract/Details

A STREAM FUNCTION METHOD FOR COMPUTING STEADY ROTATIONAL TRANSONIC FLOWS WITH APPLICATION TO SOLAR WIND-TYPE PROBLEMS


1982 1982

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Abstract (summary)

A numerical scheme has been developed to solve the quasilinear form of the transonic stream function equation. The method is applied to compute steady two-dimensional axisymmetric solar wind-type problems. A single, perfect, non-dissipative, homentropic and polytropic gas-dynamics is assumed. The four equations governing mass and momentum conservation are reduced to a single nonlinear second order partial differential equation for the stream function. Bernoulli's equation is used to obtain a nonlinear algebraic relation for the density in terms of stream function derivatives. The vorticity includes the effects of azimuthal rotation and Bernoulli's function and is determined from quantities specified on boundaries.

The approach is efficient. The number of equations and independent variables has been reduced and a rapid relaxation technique developed for the transonic full potential equation is used. Second order accurate central differences are used in elliptic regions. In hyperbolic regions a dissipation term motivated by the rotated differencing scheme of Jameson is added for stability. A successive-line-overrelaxation technique also introduced by Jameson is used to solve the equations.

The nonlinear equationfor the density is a double valued function of the stream function derivatives. The velocities are extrapolated from upwind points to determine the proper branch and Newton's method is used to iteratively compute the density. This allows accurate solutions with few grid points.

The applications first illustrate solutins to solar wind models. The equations predict that the effects of vorticity must be confined near the surface and far away the streamlines must resemble the spherically symmetric solution. Irrotational and rotational flows show this behavior. The streamlines bend toward the rotation axis for rapidly rotating models because the coriolis force is much larger than the centrifugal force.

Models of galactic winds are computed by considering the flow exterior to a surface which surrounds a uniform density oblate spheroid. Irrotational results with uniform outward mass flux show streamlines bent toward the equator and nearly spherical sonic surfaces. Rotating models for which Bernoulli's function is not constant show the sonic surface is deformed consistent with the one-dimensional theory.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences
Title
A STREAM FUNCTION METHOD FOR COMPUTING STEADY ROTATIONAL TRANSONIC FLOWS WITH APPLICATION TO SOLAR WIND-TYPE PROBLEMS
Author
KOPRIVA, DAVID ALAN
Number of pages
116
Publication year
1982
Degree date
1982
School code
0009
Source
DAI-B 43/04, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
University/institution
The University of Arizona
University location
United States -- Arizona
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
8219871
ProQuest document ID
303205673
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/303205673
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