Stream function method for computing steady rotational transonic flows with application to solar wind-type problems

Thesis/Dissertation · Fri Jan 01 04:00:00 EST 1982

OSTI ID:6337344

Kopriva, D A

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 equation for 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.

• Research Organization: Arizona Univ., Tucson (USA)
• OSTI ID: 6337344
• Country of Publication: United States
• Language: English

Related Subjects

640104* -- Astrophysics & Cosmology-- Solar Phenomena
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BERNOULLI LAW
DENSITY
FLUID FLOW
ITERATIVE METHODS
MOTION
NEWTON METHOD
NUMERICAL SOLUTION
PHYSICAL PROPERTIES
ROTATION
SOLAR ACTIVITY
SOLAR WIND
TRANSONIC FLOW
TWO-DIMENSIONAL CALCULATIONS
VELOCITY