×

Numerical solution of transonic full-potential-equivalent equations in von Mises co-ordinates. (English) Zbl 0762.76066

A new approach to calculate transonic flows is developed. A set of full- potential-equivalent equations in the von Mises coordinate system is formulated under the irrotationality and isentropic assumptions. The emphasis is placed on supercritical flow, in which the treatment of embedded shock waves is crucial to get convergent solutions. Shock jump conditions are employed and shock point operators are constructed in the body-fitting streamline coordinate system.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76H05 Transonic flows
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Murman, AIAA J. 9 pp 114– (1971)
[2] and , ’Solution of the transonic potential equation using a mixed finite difference system’, Lecture Notes in Physics, Vol. 8, Springer, Berlin, 1971, pp. 199-206.
[3] Murman, AIAA J. 12 pp 626– (1974)
[4] Hafez, AIAA J. 5 pp 786– (1977)
[5] and , ’A description of the NAE two-dimensional transonic small disturbance computer method’, NAE Laboratory Technical Report LTR-HA-39, January 1980.
[6] Jameson, Commun. Pure Appl. Math. 27 pp 283– (1974)
[7] ’Numerical solution of transonic flows with shock waves’, Symp. Transsonicum II, Springer, Berlin, 1976, pp. 384-414. · doi:10.1007/978-3-642-81005-3_43
[8] Hafez, AIAA J. 17 pp 838– (1979)
[9] Habashi, AIAA J. 20 pp 1368– (1982)
[10] Hafez, Int. j. numer. methods fluids 8 pp 1– (1988)
[11] Magnus, AIAA J. 8 pp 2157– (1970)
[12] Beam, J. Comput. Phys. 22 pp 87– (1976)
[13] Steger, AIAA J. 16 pp 676– (1978)
[14] Pulliam, J. Comput. Phys. 39 pp 343– (1981)
[15] and , ’Numerical solutions of the Euler equations by finite-volume methods using Runge-Kutta time-stepping schemes’, AIAA Paper 81-1259, 1981.
[16] Ni, AIAA J. 20 pp 1565– (1982)
[17] and , ’Finite element stream function solutions for transonic turbomachinery flows’, AIAA Paper 892-1268, 1982.
[18] Hafez, AIAA J. 21 pp 327– (1983)
[19] Habashi, Eng. Anal. 2 pp 150– (1985)
[20] Atkins, AIAA J. 23 pp 701– (1985)
[21] Barron, J. Math. Comput. Simul. 31 pp 177– (1989)
[22] Martin, Arch. Rat. Mech. Anal. 41 pp 266– (1971)
[23] Barron, Int. j. numer. methods fluids 9 pp 1183– (1989)
[24] Naeem, AIAA J. 28 pp 1836– (1990)
[25] ’A stream-function-coordinate (SFC) concept in aerodynamic shape design’, AGARD VKI Lecture Series (1990).
[26] Greywall, J. Comput. Phys. 59 pp 224– (1985)
[27] ’Experimental investigation at transonic speeds of pressure distributions over wedge and circular-arc-airfoil sections and evaluation of perforated wall interference’, NASA TN D-15, 1959.
[28] and , ’Experimental data base for computer program assessment’, AGARD AR-138, 1979, pp. A1-1-A1-36.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.