The streamline curvature technique for the numerical solution of the equations of motion for two-dimensional flow has been analysed. By considering a simple flow case an optimum damping factor for the quasi-orthogonal method was derived as a function of grid aspect ratio, Mach number, and differentiation formula, and the number of iterations required for a given accuracy was found. The stability and accuracy properties of numerical methods for finding the second derivative of a curve were also investigated, and it was found that, in this context, finite difference methods using polynomials were the best and spline methods the worst.
Get full access to this article
View all access options for this article.
References
1.
KatsanisT.‘Use of arbitrary quasi-orthogonals for calculating flow distribution in the meridional plane of a turbomachine’, NASA Tech. Note D-25461964.
2.
WoodM. D.MarlowA. V.‘The use of numerical methods for the investigation of flow in water pump impellers’, Proc. Instn mech. Engrs1966–67181 (Pt 1), 725.
3.
LanczosG.Applied Analysis (Pitman).
4.
DaviesP. O. A. L.DwyerM. J.‘A simple theory for pressure pulses in exhaust systems’, Proc. Instn. Mech. Engrs1964–65179, 365.
5.
TrengrouseG. H.SolimanM. M.‘Effect of sudden changes in flow area on pressure waves of finite amplitude’, J. mech. Engng Sci.19668, 198.
6.
DwyerM. J.‘A study of pressure waves in a pipe with reference to internal combustion engine exhaust silencers’, ISAV Rept No. 114, 1964 (August) (Southampton University).
7.
GuyT. B.‘The propagation of shock waves in discontinuous ducts’, Ph.D. thesis, Southampton University, 1969.
8.
DaviesP. O. A. L.GuyT. B.‘The diffracting shock wave’, J. Fluid Mech.1970 (to be published).
9.
DaviesP. O. A. L.GuyT. B.‘Oblique shock reflections with weak diffracting waves’, J. Fluid Mech.1970 (to be published).
10.
SkewsB. N.‘The shape of a diffracting shock wave’, J. Fluid Mech.196729, 297.
11.
GuyT. B.DaviesP. O. A. L.‘Some measurements of a shock induced vortex’, J. Fluid Mech.1970 (to be published).
12.
WhithamG. B.‘A new approach to problems of shock dynamics’, J. Fluid Mech.19572, 145.
13.
ChisnellR. F.‘The motion of a shock wave in a channel with applications to cylindrical and spherical waves’, J. Fluid Mech.19572, 286.
14.
WhithamG. B.‘A new approach to problems of shock dynamics’, J. Fluid Mech.19572, 145.
15.
OshimaK.SugayaK.YamamotoM.TolokiT.‘Diffraction of a plane shock wave around a corner’, Institute of Space and Aero Science, University of Tokyo, Rept No. 393, 1965.
